abdullah's picture
Add files using upload-large-folder tool
3a258c2 verified
raw
history blame
46 kB
1
00:00:00,720 --> 00:00:05,260
ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ู‡ุฐู‡ ู‡ูŠ ุงู„ู…ุญุงุถุฑุฉ ุงู„ุฑู‚ู… 11
2
00:00:05,260 --> 00:00:12,280
ู„ู…ุณุงู‚ ุฑูŠุงุถูŠุงุช ู…ู† ูุตู„ ู„ุทู„ุงุจ ูˆุทุงู„ุจุงุช ุงู„ุฌุงู…ุนุฉ
3
00:00:12,280 --> 00:00:16,080
ุงู„ุฅุณู„ุงู…ูŠุฉ ูƒู„ูŠุฉ ุชูƒู†ูˆู„ูˆุฌูŠุง ุงู„ู…ุนู„ูˆู…ุงุช ู‚ุณู… ุงู„ุญูˆุณุจุฉ
4
00:00:16,080 --> 00:00:22,540
ุงู„ู…ุชู†ู‚ู„ุฉ ุจุฏุฃู†ุง ุญุฏูŠุซู†ุง ููŠ ุงู„ู…ุญุงุถุฑุฉ ุงู„ุนุงุดุฑุฉ ุงู„ุณุงุจู‚ุฉ
5
00:00:22,540 --> 00:00:27,700
ุนู„ู‰ ุงู„ู„ูŠ ู‡ูˆ ุงู„-graphs ุนุฑูู†ุง ุดูˆ ู…ุนู†ู‰ ุงู„-graph ู‚ู„ู†ุง
6
00:00:27,700 --> 00:00:33,160
ุนุจุงุฑุฉ ุนู† ุงู„ู„ูŠ ู‡ูˆ set V ุงู„ู„ูŠ ู‡ูŠ ุจุชู…ุซู„ vertices ูˆ A
7
00:00:33,160 --> 00:00:37,940
ุจุชู…ุซู„ ุงู„ู„ูŠ ู‡ูŠ ุนุจุงุฑุฉ ุนู† ุงู„ุฎุทูˆุท ุงู„ู„ูŠ ุจูŠู† ุงู„ู„ูŠ ู‡ูŠ ุงู„-
8
00:00:37,940 --> 00:00:46,300
vertices ูˆุจุนุฏูŠู† ุฃุฎุฐู†ุง ุงู„ู„ูŠ ู‡ูˆ ุดูˆ ู…ุนู†ู‰ ุงู„-edge
9
00:00:46,300 --> 00:00:51,360
ุงู„ู„ูŠ ู‡ูˆ ุงู„ุฎุท ูˆุดูˆ ู…ุนู†ู‰ ุงู„ู„ูŠ ู‡ูˆ ุงู„-neighborhood
10
00:00:51,360 --> 00:00:55,700
ูˆุจุนุฏูŠู† ุงู„ู„ูŠ ู‡ูˆ ุดูˆ .. ู‚ู„ู†ุง ุดูˆ ู…ุนู†ู‰ ุฃู†ู‡ two edges ุชูƒูˆู†
11
00:00:55,700 --> 00:01:02,960
adjacent ูˆุฃูŠุถุง ุนุฑูู†ุง ุงู„ู„ูŠ ู‡ูˆ ุดูˆ ู…ุนู†ู‰ ุงู„-degree
12
00:01:02,960 --> 00:01:08,340
ู„ู„-vertex ูˆ .. ูˆู‚ู„ู†ุง ุงู„-vertex ุงู„ู„ูŠ ุงู„-degree ู„ู‡
13
00:01:08,340 --> 00:01:12,900
zero ู‚ู„ู†ุง isolated ูˆุฃุฎุฐู†ุง ุฃู…ุซู„ุฉ ุนู„ู‰ ู‡ูŠูƒ ู„ุฃู…ุซู„ุฉ
14
00:01:12,900 --> 00:01:18,300
ุงู„ู„ูŠ ุฃู…ุงู…ู†ุง ู‡ุฐู‡ ูˆุนู„ู‰ ุงู„-degree ุฅู„ู‰ ุขุฎุฑู‡ ูˆุงู†ุชู‚ู„ู†ุง
15
00:01:20,810 --> 00:01:24,030
ุทุจุนุง ูƒู†ุง ุญุงูƒูŠู†ุง ุนู† ุงู„ู€undirected graph ุจุนุฏูŠู†
16
00:01:24,030 --> 00:01:28,650
ุฃุฎุฐู†ุง ุฃู…ุซู„ุฉ ุนู„ู‰ ูƒู„ ู‡ุฐู‡ ุงู„ู…ูˆุถูˆุนุงุช ูˆุฌุฆู†ุง ุฃุฎุฐู†ุง ุงู„ู„ูŠ
17
00:01:28,650 --> 00:01:33,270
ู‡ูˆ ุงู„ู†ุธุฑูŠุฉ ุงู„ู„ูŠ ุจุชู‚ูˆู„ ุฏุงุฆู…ุง ุงู„ู„ูŠ ู‡ูˆ ุงู„ู…ุฌู…ูˆุน ุงู„ู„ูŠ
18
00:01:33,270 --> 00:01:37,050
ู‡ูˆ ุงู„-degree ู„ู„-vertices ุนู„ู‰ ูƒู„ ุงู„-vertices ุงู„ู„ูŠ
19
00:01:37,050 --> 00:01:41,650
ููŠ ุงู„-V ุจุชุณุงูˆูŠ 2 ููŠ ุญุงุตู„ ุถุฑุจ ุงู„ู„ูŠ ู‡ูˆ ุนุฏุฏ ุงู„ุฎุทูˆุท ุฃูˆ
20
00:01:41,650 --> 00:01:46,570
ุนุฏุฏ ุงู„-edges ุงู„ู„ูŠ ููŠ ุงู„ุดูƒู„ ูˆุจุนุฏูŠู† ุฃุฎุฐู†ุง ุฃู…ุซู„ุฉ ุนู„ู‰
21
00:01:46,570 --> 00:01:51,570
ู‡ูŠูƒ ูˆุฃุฎุฐู†ุง ุจุนุฏ ู‡ูŠูƒ ุดูˆ ู…ุนู†ู‰ .. ุดูˆ ู…ุนู†ู‰ ุงู„ู„ูŠ ู‡ูˆ ุงู„-
22
00:01:51,570 --> 00:01:54,690
directed graph ุงู„ู„ูŠ ุจูŠูƒูˆู† .. ู‚ู„ู†ุง ุจูŠุณูŠุฑ ุงู„ู„ูŠ ู‡ูˆ
23
00:01:54,690 --> 00:02:00,370
ุงู„ุฎุท ุงู„ู„ูŠ ู‡ูˆ directed from ู†ู‚ุทุฉ ุฅู„ู‰ ู†ู‚ุทุฉ ุฃุฎุฑู‰
24
00:02:00,370 --> 00:02:05,990
ูˆุฃุฎุฐู†ุง ุงู„ู„ูŠ ู‡ูˆ ุฃู…ุซู„ุฉ ุนู„ูŠู‡ู… ูˆุฃุฎุฐู†ุง ุดูˆ ุงู„-degree ุงู„ู„ูŠ
25
00:02:05,990 --> 00:02:09,990
ู‡ูŠ ุงู„ุฎุงุฑุฌุฉ ูˆุงู„ู€degree ุงู„ุฏุงุฎู„ุฉ ูˆุฃุฎุฐู†ุง ุงู„-homework
26
00:02:09,990 --> 00:02:13,690
ูˆุงู„ูŠูˆู… ุฅู† ุดุงุก ุงู„ู„ู‡ ุจุฏู†ุง ู†ุจุฏุฃ ู†ุญูƒูŠ ุนู† ุงู„ู„ูŠ ู‡ูˆ
27
00:02:13,690 --> 00:02:18,210
ุงู„ู…ูˆุถูˆุนุงุช ุงู„ู…ูƒู…ู„ุฉ ู„ู„ูŠ ุญูƒูŠู†ุงู‡ุง ุงู„ู„ูŠ ู‡ูŠ ุฎู„ูŠู†ุง ู†ุญูƒูŠ
28
00:02:18,210 --> 00:02:22,510
ุนู† ุญุงุฌุฉ ุงุณู…ู‡ุง subigraph subigraph ูŠุนู†ูŠ ุฌุฒุก ู…ู†
29
00:02:22,510 --> 00:02:25,930
ุงู„-igraph ุฌุฒุก ู…ู† ุงู„-igraph ุทุจูŠุนู‰ ู†ุดูˆู ุฅูŠุด ุนุฑูู†ุงู‡
30
00:02:26,460 --> 00:02:31,860
ุจู‚ูˆู„ ู„ูˆ ูƒุงู† ุนู†ุฏูŠ graph g1 is a sub graph ูŠุนู†ูŠ ู‡ุฐุง
31
00:02:31,860 --> 00:02:36,320
g1 ุจู†ู‚ูˆู„ ุนู†ู‡ sub graph ู…ู† ู…ูŠู† of another graph g
32
00:02:36,320 --> 00:02:41,040
ูŠุนู†ูŠ g1 ุนุจุงุฑุฉ ุนู† sub graph ุฃูˆ graph ุฌุฒุฆูŠ ู…ู† ุงู„-
33
00:02:41,040 --> 00:02:46,080
graph g if and only if the vertex and edges sets
34
00:02:46,080 --> 00:02:49,730
of g1 are respectively subsets of the vertex and
35
00:02:49,730 --> 00:02:53,730
edges of G ู†ุญู† ู†ุชูุงุฌุฃ ุฃู† G ูŠูƒูˆู† ู…ูƒูˆู† ู…ู† ุดุบู„ ุซุงู†ูŠ
36
00:02:53,730 --> 00:02:59,270
ู…ู† vertices ู…ู† vertices ูˆู…ู† ุฎุทูˆุท ุฅุฐุง ุจู†ู‚ูˆู„ ุฅู† G1
37
00:02:59,270 --> 00:03:04,450
sub graph ู…ู† G ุฅุฐุง ูƒุงู† ูƒู„ ุงู„-vertices ุงู„ู„ูŠ ููŠ G1
38
00:03:04,450 --> 00:03:11,610
ู…ูˆุฌูˆุฏุฉ ููŠ vertices ููŠ G ููŠ ุงู„-V ุชุจุนุชู‡ ูˆูƒู„ ุงู„ุฎุทูˆุท
39
00:03:11,610 --> 00:03:15,190
ุงู„ู€edges ุงู„ู„ูŠ ููŠ ุงู„ู€ .. ุงู„ู„ูŠ ููŠ ุงู„ู€G1 ุงู„ู„ูŠ ูƒู†ุง
40
00:03:15,190 --> 00:03:20,070
ู†ุณู…ูŠู‡ุง ุฅูŠู‡ ู‡ูŠ ุนุจุงุฑุฉ ุนู† ุฎุทูˆุท ู…ูˆุฌูˆุฏุฉ ููŠ ู…ูŠู† ููŠ ุงู„ู€G
41
00:03:20,070 --> 00:03:24,950
ุงู„ุฃุตู„ูŠุฉ ุงู„ุขู† ู†ูŠุฌูŠ ู†ุฃุฎุฐ ุฃู…ุซู„ุฉ ุงู„ู„ูŠ ู‡ูŠ ุฃู…ุงู…ู†ุง ู‡ุฐู‡
42
00:03:24,950 --> 00:03:27,570
ุนู†ุฏูŠ ุงู„-graph G ู‡ุฐู‡ ูˆู‡ุฐุง ุงู„-graph G ู‡ุฐู‡ ุงู„-
43
00:03:27,570 --> 00:03:31,290
vertices ูƒู„ู‡ุง ู…ูˆุฌูˆุฏุฉ ุนู†ุฏูŠ ูˆู‡ุฐู‡ ุงู„ุฎุทูˆุท ุงู„ู„ูŠ ุจูŠู†ู‡ุง
44
00:03:31,290 --> 00:03:34,550
ุงู„ู„ูŠ ู‡ูŠ ุงู„-edges ุงู„ู„ูŠ ุจูŠู†ู‡ุง ุงู„ู„ูŠ ู‡ู†ุฌูŠ ู†ุทู„ุนู‡ุง
45
00:03:34,550 --> 00:03:42,870
ู„ู‡ุฐุง ู‡ุฐุง V4 ู‡ูŠ ู…ูˆุฌูˆุฏุฉ ู‡ู†ุง V4V3 ู‡ูŠู‡ุง ุฌุงูŠ ู…ู† ู‡ู†ุง V7
46
00:03:42,870 --> 00:03:48,090
ู‡ูŠู‡ุง ู…ู† ู‡ู†ุง V6 ู‡ูŠู‡ุง ู…ู† ู‡ู†ุง ุงู„ุฎุทูˆุท ุงู„ู„ูŠ ุจูŠู†ู‡ู… V7 ูˆ
47
00:03:48,090 --> 00:03:58,230
V6 ู‡ูŠ V7 ูˆ V6 ู…ูˆุฌูˆุฏ V6 ูˆ V3 ู‡ูŠ ู…ูˆุฌูˆุฏ V4 ูˆ V3 ู‡ูŠ V4
48
00:03:58,230 --> 00:04:04,770
ูˆ V3 ู…ูˆุฌูˆุฏ ุฅุฐุง ู‡ุฐุง ุงู„-graph ู‡ูˆ ุนุจุงุฑุฉ ุนู† ุฌุฒุก ู…ู† ู‡ุฐุง
49
00:04:04,770 --> 00:04:08,510
ู„ุฃู† ุงู„ุฎุทูˆุท ู‡ุฐู‡ ู…ูˆุฌูˆุฏุฉ ููŠ ุงู„-graph ุงู„ุฃุตู„ูŠ ูˆุงู„ู€
50
00:04:08,510 --> 00:04:12,530
vertices ู…ูˆุฌูˆุฏุฉ ููŠ ุงู„-graph ุงู„ุฃุตู„ูŠ ุนุดุงู† ู‡ูŠูƒ ุจู†ุณู…ูŠ
51
00:04:12,530 --> 00:04:17,150
ู‡ุฐุง sub graph ู…ู† ู‡ุฐุง ู†ุดูˆู ุงู„-graph ุงู„ุซุงู†ูŠุŒ ู„ุงุญุธูˆุง
52
00:04:17,150 --> 00:04:25,280
V2 ู‡ูŠ ู…ูˆุฌูˆุฏุฉ V3 ู‡ูŠ V3 V6
53
00:04:25,280 --> 00:04:33,000
V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ
54
00:04:33,000 --> 00:04:33,140
V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6
55
00:04:33,140 --> 00:04:34,080
ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ
56
00:04:34,080 --> 00:04:34,920
V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ
57
00:04:34,920 --> 00:04:47,760
V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6 V7 ู‡ูŠ V6
58
00:04:47,760 --> 00:04:53,380
V7 ุงู„ุขู† ุจุฏู†ุง ู†ุฃุฎุฐ ุงู„ู„ูŠ ู‡ูˆ some special simple
59
00:04:53,380 --> 00:04:58,160
graphs ุฃูˆ ุญุงุฌุฉ ุจู†ุณู…ูŠู‡ุง complete graphs ุจุฏู†ุง ู†ุฑุฌุน ู„
60
00:04:58,160 --> 00:05:03,420
ุงู„ู„ูŠ ู‡ูˆ ุงู„-graphs ูˆุจุฏู†ุง ู†ุณู…ูŠ ุจุนุถ ุงู„-graphs ู„ูŠุด
61
00:05:03,420 --> 00:05:09,820
ุจู†ุณู…ูŠู‡ุง complete graph ุจู†ุณู…ูŠู‡ ูˆู†ุดูˆู ู„ูŠุด ุงู„-graph
62
00:05:09,820 --> 00:05:14,340
ุจู†ุณู…ูŠู‡ complete ุจู†ุงุฎุฐ ุฃู†ูˆุงุน ู…ุนูŠู†ุฉ ุฎู„ูŠู†ุง ู†ุดูˆู ุฅูŠุด
63
00:05:14,340 --> 00:05:18,280
ุงู„ู…ุฌูˆู„ุฉ for any positive integer n ู„ูˆ ูƒุงู† n ุนุจุงุฑุฉ
64
00:05:18,280 --> 00:05:20,840
ุนู† positive integer ูŠุนู†ูŠ ูˆุงุญุฏ ุฃูˆ ุงุซู†ูŠู† ุฃูˆ ุซู„ุงุซุฉ
65
00:05:20,840 --> 00:05:24,280
ุฃูˆ ุฃุฑุจุนุฉ ุฅู„ู‰ ุขุฎุฑู‡ ู‡ูŠ the complete graph on n
66
00:05:24,280 --> 00:05:29,620
vertices ูŠุนู†ูŠ ู„ู…ุง ู†ู‚ูˆู„ ุนู† ุงู„-graph ุงู„ู„ูŠ ููŠู‡ n
67
00:05:29,620 --> 00:05:30,220
vertices
68
00:05:33,500 --> 00:05:38,600
ูŠุนู†ูŠ ููŠ ูƒู… ุฑุฃุณ ููŠ N ู…ู† ุงู„ุฑุคูˆุณ ุจู‚ูˆู„ ุฏู‡ complete
69
00:05:38,600 --> 00:05:43,380
graph on N vertices denote KN ูŠุนู†ูŠ ุงู„ุขู† ุจุฏู†ุง ู†ุณู…ูŠ
70
00:05:43,380 --> 00:05:51,240
ุงู„-KN ู‡ุฐุง ูŠุฑู…ุฒ ุฅู„ู‰ complete graph with n vertices
71
00:05:51,240 --> 00:05:57,700
ููŠ ุฅูŠุด ู…ุงู„ู‡ n ู…ู† ุงู„ุฑุคูˆุณ ุทุจุนุง ุดูˆููˆุง ู‡ุฐุง ูƒุฃู† is a
72
00:05:57,700 --> 00:06:02,400
graph with n vertices ูŠุนู†ูŠ ู‡ุฐุง ูƒุฃู† ุนุจุงุฑุฉ ุนู† graph
73
00:06:02,400 --> 00:06:06,760
with n vertices every two of which are adjacent
74
00:06:06,760 --> 00:06:11,380
ูŠุนู†ูŠ ูƒู„ ุงุซู†ูŠู† ู…ู† ุงู„-vertices adjacent ู…ุชุฌุงูˆุฑุชุงู†
75
00:06:11,380 --> 00:06:14,420
ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู†
76
00:06:14,420 --> 00:06:15,000
ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู†
77
00:06:15,000 --> 00:06:19,260
ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู†
78
00:06:19,260 --> 00:06:23,500
ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ู…ุชุฌุงูˆุฑุชุงู† ุงู‡ูŠ ุนู†ุฏูŠ ูƒุฃู†ูŠ ููŠ ู†ู‚ุทุชูŠู†
79
00:06:23,500 --> 00:06:29,260
ุงู„ู†ู‚ุทุชูŠู† ู‡ุฏูˆู„ ููŠ ุงู„ุชู†ุชูŠู† ุจูŠู†ู‡ุง ุฎุท ู…ุง ููŠุด ุฃูŠ ู†ู‚ุทุฉ
80
00:06:29,260 --> 00:06:34,440
ููŠ ุฏุงุฎู„ ุงู„ูƒู†ุชูŠู† ู…ุง ููŠุด ุจูŠู†ู‡ุง ูˆุจูŠู† ุงู„ุจุงู‚ูŠุงุช ุฎุทูˆุท
81
00:06:34,440 --> 00:06:42,900
ุนุดุงู† ู‡ูŠูƒ ุจู†ุณู…ูŠ ู‡ุฐุง complete graph ู…ู† ุงู„ู†ูˆุน K2 ู†ุดูˆู
82
00:06:42,900 --> 00:06:50,440
ู†ูˆุน ุขุฎุฑ K3 K3 K3 ุฃุดู…ู„ ููŠู‡ ุซู„ุงุซ ุฑุคูˆุณ ู‡ุฐู‡ ุฑุฃุณ ู‡ุฐู‡
83
00:06:50,440 --> 00:06:55,960
ุฑุฃุณุงู† ู‡ุฐู‡ ุซู„ุงุซุฉ ู„ุงุญุธุช ุซู„ุงุซ ุฑุคูˆุณ ูุนู„ุง ู‡ุฐุง ูˆู‡ุฐุง ุจูŠู†
84
00:06:55,960 --> 00:06:59,860
ุงู„ุฎุท ูˆู‡ุฐุง ูˆู‡ุฐุง ุจูŠู† ุงู„ุฎุท ูˆู‡ุฐุง ูˆู‡ุฐุง ุจูŠู† ุงู„ุฎุท ูŠุนู†ูŠ ูƒู„
85
00:06:59,860 --> 00:07:05,920
ุงู„ุฑุคูˆุณ are adjacent ูŠุนู†ูŠ ู…ุง ู„ู‡ู† ูƒู„ ุงู„ุฑุคูˆุณ ุงู„ู„ูŠ ู‡ูŠ
86
00:07:05,920 --> 00:07:09,380
ุจูŠู†ู‡ู† ูˆุจูŠู† ุจุนุถ ุฎุทูˆุท ุนุดุงู† ู‡ูŠูƒ ุจู†ุณู…ูŠู‡ุง ุฏู‡ Complete
87
00:07:09,380 --> 00:07:13,640
Graph ู‡ุฐุง ุงู„ู†ูˆุน ู…ู† ุงู„-graphs ุงู„ู„ูŠ ุฒูŠ ู‡ูŠูƒ ุงู„ู„ูŠ
88
00:07:13,640 --> 00:07:17,240
ูƒู†ุชูŠู† ูƒุชู„ุงุชุฉ ุงู„ู„ูŠ ููŠ ุนุฏุฏ ุงู„ู„ูŠ ู‡ูˆ ุงุซู†ูŠู† ุฃูˆ ุนุฏุฏ
89
00:07:17,240 --> 00:07:21,860
ุซู„ุงุซุฉ ุฃูˆ ุจุนุฏ ุดูˆูŠุฉ ุฃุฑุจุนุฉ ุฃูˆ ุฎู…ุณุฉ ุฃูˆ ุณุชุฉ ูˆุจูƒูˆู† ุจุฎุงุตูŠุฉ
90
00:07:21,860 --> 00:07:28,320
ุฃู†ู‡ ูƒู„ ุงุซู†ูŠู† ูƒู„ ู†ู‚ุทุชูŠู† ุจูŠู† ุงู„ุฎุท ุจู†ุณู…ูŠู‡ ุงู„ู„ูŠ ู‡ูˆ
91
00:07:28,320 --> 00:07:32,990
Complete Graph ู…ู† ุงู„ู†ูˆุน KN ู†ุฌูŠ ู„ู€ K ุฃุฑุจุนุฉ K ุฃุฑุจุนุฉ
92
00:07:32,990 --> 00:07:36,110
ุงู„ู„ูŠ ู‡ูˆ ูˆุงุญุฏ ุงุซู†ูŠู† ุซู„ุงุซุฉ ุฃุฑุจุนุฉ ููŠู‡ุง ุฃุฑุจุน ุนูŠุงุด ู†ู‚ุงุท
93
00:07:36,110 --> 00:07:43,330
ุงู„ุฃุฑุจุน ู†ู‚ุงุท ูƒู„ู‡ู… ุจูŠู† ู‡ุฐู‡ ูˆู‡ุฐู‡ ุฎุท ูˆุจูŠู†ู‡ุง ูˆุจูŠู†ู‡ุง
94
00:07:43,330 --> 00:07:48,510
ุฏูŠ ุฎุท ูˆุจูŠู†ู‡ุง ูˆุจูŠู†ู‡ุง ุฏูŠ ุฎุท ูŠุนู†ูŠ ูƒู„ ุงู„ู†ู‚ุงุท ุงู„ู„ูŠ ู‡ู…
95
00:07:48,510 --> 00:07:52,970
adjacent ู„ุจุนุถ ุนุดุงู† ู‡ูŠูƒ ุจู†ุณู…ูŠู‡ graph ุฅุฐุง ุงู„-
96
00:07:52,970 --> 00:07:58,890
complete graph ู‡ูˆ graph ุนุงุฏูŠ ูƒู„ ู†ู‚ุทุชูŠู† ููŠู‡ adjacent
97
00:07:58,890 --> 00:08:03,590
ูŠุนู†ูŠ ูƒู„ ู†ู‚ุทุชูŠู† ููŠู‡ graph ุญุงู„ุฉ ุฎุงุตุฉ ู…ู† ู‡ุฐูˆู„ ุงู„-
98
00:08:03,590 --> 00:08:08,850
complete graph ุงู„ู„ูŠ ู‡ูŠ ุนุงุฆู„ุฉ ู…ู† ุงู„-graphs ุงุณู…ู‡ุง Kn
99
00:08:08,850 --> 00:08:14,890
ุฅูŠุด ุงู„-Kn ู‡ุฐู‡ ุงู„ู„ูŠ ู‡ูŠ ุนุฏุฏู‡ุง n ู…ู† ุงู„ู„ูŠ ู‡ูˆ ุงู„-
100
00:08:14,890 --> 00:08:20,000
vertices ููŠู‡ุงุŸ ูˆุจูŠุนู…ู„ูŠู† complete graph ูŠุนู†ูŠ ูƒู„
101
00:08:20,000 --> 00:08:25,820
ุงู„ู†ู‚ุงุท are adjacent ุฏู‡ ู†ุดูˆู ุงู„ู„ูŠ ุจุนุฏู‡ุง ู‡ุฐู‡ K ุฎู…ุณุฉ
102
00:08:25,820 --> 00:08:30,140
ู…ุซู„ุง ุจุฎู…ุณุฉ ู‡ุฐู‡ ุนู†ุฏูŠ ุฎู…ุณ ู†ู‚ุงุท ูˆุงุญุฏุฉ ุงุซู†ูŠู† ุซู„ุงุซุฉ
103
00:08:30,140 --> 00:08:32,900
ุฃุฑุจุนุฉ ุฎู…ุณุฉ ูˆุงุถุญ ุฃู† ูƒู„ ุงู„ู†ู‚ุงุท ูƒู„ ูˆุงุญุฏุฉ ุจูŠุทู„ุน ู…ู†ู‡ุง
104
00:08:32,900 --> 00:08:37,940
ุฃุฑุจุน ุฎุทูˆุท ู„ู„ุขุฎุฑูŠู† ูุนุดุงู† ู‡ูŠูƒ ุจู†ุณู…ูŠู‡ุง complete graph
105
00:08:37,940 --> 00:08:43,680
ู…ู† ุงู„ู†ูˆุน K ู„ูˆ ูˆุงุญุฏ ุจุฏู‡ ูŠุฑุณู… K6 ุจุชู‚ุฏุฑ ุชุฑุณู…ู‡ุง ุจู†ูุณ
106
00:08:43,680 --> 00:08:48,060
ุงู„ุงุณู… ูˆ K7 ุทุจุนุง ุจุชุบู„ุจ ุดูˆูŠุฉ ู„ูƒู† ุจุชุธู„ู‡ุง ููŠ ู†ูุณ
107
00:08:48,060 --> 00:08:54,800
ุงู„ู†ุทุงู‚ ู‡ุฐู‡ ุจู†ุณู…ูŠู‡ุง complete graphs ุฃูˆ ู…ุซู„ ุนู„ู‰ ุงู„-
108
00:08:54,800 --> 00:09:00,240
complete graphs ุงู„ู„ูŠ ู‡ูŠ ุงู„ุนุงุฆู„ุฉ ุงู„ู„ูŠ ุณู…ูŠู†ุงู‡ุง Kn ุนู†ุฏ
109
00:09:00,240 --> 00:09:03,280
K ูˆุงุญุฏ ุจุฑุถู‡ ู†ุนุชุจุฑู‡ complete ู„ูŠุดุŸ ู„ุฃู† ุงู„-complete
110
00:09:03,280 --> 00:09:07,740
graph ู…ุง ูŠูƒูˆู†ุด ููŠู‡ ู†ู‚ุทุชูŠู† ู…ุด adjacent ู…ุง ููŠุด ููŠู‡
111
00:09:07,740 --> 00:09:10,840
ู†ู‚ุทุชูŠู† ู…ุด adjacent ู„ุฃู†ู‡ ุฃุตู„ุง ู‡ูŠ ุงู„ู†ู‚ุทุฉ ุจุณ ู„ุญุงู„ู‡ุง
112
00:09:10,840 --> 00:09:17,730
ุนุดุงู† ู‡ูŠูƒ ุจู†ุณู…ูŠู‡ุง ุงู„ู„ูŠ ู‡ูŠ ุจุฑุถู‡ complete graph K1, K2,
113
00:09:17,850 --> 00:09:22,130
K3, K4, K5 ุฅู„ู‰ ุขุฎุฑู‡ ู‡ูŠ ุฒู…ู†ุชู‡ ุจุชุงุนู†ุง ุงู„ุขู† ุจุฏู†ุง ู†ูŠุฌูŠ
114
00:09:22,130 --> 00:09:26,810
ู†ูˆุน ุซุงู†ูŠ ู„ู€ graphs ุญุงุฌุฉ ุงุณู…ู‡ุง ุงู„-cycles ู…ุงุดูŠ ุฅูŠุด ุงู„-
115
00:09:26,810 --> 00:09:31,850
cycles ุงู„ู„ูŠ ู‡ูŠ ูˆุงู„-wheels ุงู‡ ุฅูŠุด ู†ุดูˆู ุฅูŠุด ุงู„-
116
00:09:31,850 --> 00:09:37,900
cycle ูˆุฅูŠุด ุงู„-wheel ุงู„ุขู† cycle cn ุฏู‡ ู†ุฑู…ุฒ ู„ู‡ ุจุจุฑู†ุงู…ุฌ
117
00:09:37,900 --> 00:09:41,220
cn ุจุนุฏ ุฅุฐู†ูƒู… ูŠุนู†ูŠ ููŠ ุนู†ุฏูŠ n ุฃูƒุจุฑ ุฃูˆ ุชุณุงูˆูŠ ุซู„ุงุซุฉ ูŠุนู†ูŠ
118
00:09:41,220 --> 00:09:47,380
ุนู†ุฏูŠ cycle c3 ูˆ c4 ูˆ c5 ูˆ c6 ุฅู„ู‰ ู…ุง ู„ุง ู†ู‡ุงูŠุฉ
119
00:09:47,380 --> 00:09:51,900
consists of n vertices ูŠุนู†ูŠ ุงู„-cn ู‡ุฐู‡ ุจุฑุถู‡ ุจุชุญุชูˆูŠ
120
00:09:51,900 --> 00:09:57,860
ุนู„ู‰ ุฅูŠู‡ ุนู„ู‰ n ู…ู† ุงู„-vertices ู…ุงุฐุง ู†ุณู…ูŠู‡ Cycle ู„ู…ุง
121
00:09:57,860 --> 00:10:02,960
ู†ูƒูˆู† ุชุญู‚ู‚ ู…ุง ูŠู„ูŠ ุงู„-CNN Consists Of N Vertices
122
00:10:02,960 --> 00:10:08,480
V1 ูˆ V2 ูˆ VN And Edges ูˆุงู„ู€Edges ุฅูŠุด ู…ุง ู„ู‡ุง V1 ูˆ
123
00:10:08,480 --> 00:10:13,890
V2 ูŠุนู†ูŠ ุฎุท ุจูŠู† V1 ูˆ V2 ูˆุฎุท ุจูŠู† V2 ูˆ V3 ูˆุฎุท ุจูŠู† V3
124
00:10:13,890 --> 00:10:19,330
ูˆ V4 ู„ู…ุง ุฃุตู„ ุนู†ุฏ ุฎุท ุจูŠู† ุงู„ู„ูŠ ู‡ูŠ ุงู„ู†ู‚ุทุฉ ุงู„ุฃุฎูŠุฑุฉ VN
125
00:10:19,330 --> 00:10:25,430
ูˆุจุฑุฌุน ู„ู…ูŠู† ู„ู„ู€V1 ูˆูƒุฃู† ุฅูŠุด ุจุณูƒุฑ ูˆุจุนู…ู„ู‡ cycle ุฒูŠ
126
00:10:25,430 --> 00:10:30,190
ุฏุงุฆุฑุฉ ุฃูˆ ุงู„ู„ูŠ ู‡ูˆ ุฏูˆุฑุฉ ูƒุงู…ู„ุฉ ู…ุงุดูŠ the cycles C3,
127
00:10:30,330 --> 00:10:38,350
C4, C5, C6 are displaced ุงู†ูุฌุงุฑุง ู‡ูŠ ูˆู‡ุฐู‡ ูˆู‡ุฐู‡ ุงู„ู„ูŠ
128
00:10:38,350 --> 00:10:46,690
ู‡ูŠ V1 V2 V2 V3 V3 V1 ุฅุฐุงู‹ ู‡ุฐุง cycle ุตุงุฑ ุงู„ุขู† ู‡ุฐุง
129
00:10:46,690 --> 00:10:50,170
ุงู„ graph complete ุฃู‡ complete ู„ุฃู†ู‡ ูƒู„ ู…ุบุทูŠู†
130
00:10:50,170 --> 00:10:54,850
adjacent ูŠุนู†ูŠ ุงู„ cycle ู…ู…ูƒู† ุชูƒูˆู† complete ูŠุนู†ูŠ
131
00:10:54,850 --> 00:10:59,730
ู…ุซุงู„ ุนู„ู‰ complete graph ู†ุฌูŠ ู„ู„ูŠ ุจุนุฏู‡ุง C4 ู‡ูŠ ู…ู† ุนู†ุฏ
132
00:10:59,730 --> 00:11:03,010
ุงู„ู†ู‚ุทุฉ ุงู„ุฃูˆู„ู‰ ู„ู„ุชุงู†ูŠุฉ ููŠ ุฎุท ูˆ ู…ู† ุงู„ุชุงู†ูŠุฉ ู„ู„ุชุงู„ุชุฉ ูˆ
133
00:11:03,010 --> 00:11:05,770
ู…ู† ุงู„ุชุงู„ุชุฉ ู„ู„ุฑุงุจุนุฉ ูˆ ู…ู† ุงู„ุฑุงุจุนุฉ ู„ู„ุฃูˆู„ู‰ ุฑุฌุนุช ูŠุนู†ูŠ
134
00:11:05,770 --> 00:11:10,190
ุฃู‚ูู„ุช ุงู„ุฏุงุฆุฑุฉ ุฃูˆ ุฃู‚ูู„ุช ุงู„ู„ูŠ ู‡ูŠ ุงู„ cycle ู‡ุฐุง ุจู†ุณู…ูŠู‡
135
00:11:10,190 --> 00:11:13,590
ุจุฑุถู‡ cycle ู‡ู„ ู‡ุฐุง completeุŸ ู„ุง ู…ุด complete ู„ูŠุด ู…ุด
136
00:11:13,590 --> 00:11:16,850
completeุŸ ู„ุฃู† ู‡ุฐูŠ ูˆ ู‡ุฐุง ุงู„ู†ู‚ุทุฉ they are not
137
00:11:16,850 --> 00:11:20,850
adjacent ู„ุฃู†ู‡ ู…ุงููŠุด ุจูŠู† ุงู„ุฎุท ูˆ ู‡ุฐูŠ ูƒู…ุงู† ูˆ ู‡ุฐูŠ ุฅุฐุง
138
00:11:20,850 --> 00:11:24,090
ู‡ูŠ ููŠ ุนู†ุฏ ุงู„ cycle ู„ูŠุณ ุดุฑุท ุฃู† ุชูƒูˆู† ุฅูŠุด ู…ุงู„ู‡ุง
139
00:11:24,090 --> 00:11:28,450
complete ุงู‚ุฑุฃ ุงู„ุขู† ู†ุฌูŠ ู„ู€ C5 C5 ุจู†ูุณ ุงู„ุฃุณู„ูˆุจ ููŠู‡ุง
140
00:11:28,450 --> 00:11:31,330
ุฎู…ุณ ู†ู‚ุงุท ุงู„ุฎู…ุณ ู†ู‚ุงุท ุจุชุจุฏุฃ ู…ู† ุนู†ุฏ ุงู„ู†ู‚ุทุฉ ุงู„ุฃูˆู„ู‰ ูˆ
141
00:11:31,330 --> 00:11:33,670
ุจุชุจุฏุฃ ู„ู„ุชุงู†ูŠุฉ ุฃูˆ ู„ู„ุชุงู„ุชุฉ ุฃูˆ ู„ู„ุฑุงุจุนุฉ ุฃูˆ ู„ู„ุฎุงู…ุณุฉ ุฃูˆ
142
00:11:33,670 --> 00:11:37,770
ู„ู„ุณุงุฏุณุฉ ุงู„ู„ูŠ ุงู„ุฎู…ุณุฉ ุจุชุฑุฌุน ู„ู…ูŠู† ู„ู„ู†ู‚ุทุฉ ุงู„ุฃูˆู„ู‰
143
00:11:37,770 --> 00:11:42,770
ูุจุชุนู…ู„ ู„ูŠู‡ cycle ุงู„ู„ูŠ ู‡ูŠ ุจุชุณูƒุฑ ุงู„ู„ูŠ ู‡ูŠ ุงู„ุฏูˆุฑุฉ ุงู„ุขู†
144
00:11:42,770 --> 00:11:47,890
C6 ุจู†ูุณ ุงู„ุฃุณู„ูˆุจ ููŠู‡ุง ุณุช ู†ู‚ุงุท ูƒู„ ู†ู‚ุทุฉ ุงู„ V1 ุจุชุฑูˆุญู‡ุง
145
00:11:47,890 --> 00:11:52,150
V2 V2 ุชู„ุงุชุฉ V3 ุฃูˆ V4 ู…ุงูู‡ู…ุด ู…ุนู†ุงุช ุจุชุฑูˆุญ ูŠุนู†ูŠ ุจูŠู†
146
00:11:52,150 --> 00:12:02,610
ุงู„ุฎุท V4 V5 V5 V6 V6 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
147
00:12:02,610 --> 00:12:03,510
V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
148
00:12:03,510 --> 00:12:06,110
V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
149
00:12:06,110 --> 00:12:06,890
V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
150
00:12:06,890 --> 00:12:08,650
V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
151
00:12:08,650 --> 00:12:12,150
V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
152
00:12:12,150 --> 00:12:15,610
V1 V1
153
00:12:15,980 --> 00:12:21,720
when we add an additional vertex to cycle CN ูŠุนู†ูŠ
154
00:12:21,720 --> 00:12:29,280
ุฅูŠุด ุจู†ุฌูŠุจุŸ ุจู†ุฌูŠุจ ู‡ูŠ ุงู„ cycle ูˆ ุจู†ุถูŠู ู„ู‡ุง ู†ู‚ุทุฉ ุฅูŠุด
155
00:12:29,280 --> 00:12:33,040
ุงู„ู†ู‚ุทุฉ ุฏูŠ ู…ุงู„ู‡ุงุŸ ู†ุดูˆู ุฅูŠุด ู…ุงู„ู‡ุง we add an
156
00:12:33,040 --> 00:12:36,260
additional vertex to cycle CN for N ุฃูƒุจุฑ ุณูˆุงุก
157
00:12:36,260 --> 00:12:41,940
ุซู„ุงุซุฉ and connect this new vertex to each of the
158
00:12:41,940 --> 00:12:48,410
vertices in CN by new edges ุฅุฐุง ุงู„ุขู† ู…ุง ู‡ูŠ ุฅู„ุง
159
00:12:48,410 --> 00:12:52,570
cycle ุจู†ุญุท ุฌูˆุงุชู‡ุง ู†ู‚ุทุฉ ุฃูˆ ุฌู†ุจู‡ุง ู†ู‚ุทุฉ ููŠ ุงู„ู…ูƒุงู†
160
00:12:52,570 --> 00:12:56,010
ุงู„ู…ู†ุงุณุจ ุฌูˆุงุชู‡ุง ุฃูุถู„ ูŠุนู†ูŠ ุจุชูƒูˆู† ุฃุญู„ู‰ ููŠ ุงู„ุฑุณู… ูˆ
161
00:12:56,010 --> 00:13:01,590
ุจู†ูˆุตู„ ู…ู† ุงู„ู†ู‚ุทุฉ ู‡ุฐู‡ ุฎุทูˆุท ู„ูƒู„ ุฃูˆ edges ู„ูƒู„ ู…ู† ุงู„
162
00:13:01,590 --> 00:13:05,390
vertices ุงู„ู„ูŠ ู…ูˆุฌูˆุฏุฉ ู‡ุฐู‡ ุงู„ู†ู‚ุทุฉ ู‡ูŠุนู…ู„ู†ุง ุงู„ู„ูŠ ู‡ูˆ
163
00:13:05,390 --> 00:13:09,810
edge ูˆู‡ูŠ edge ูˆู‡ูŠ edge ู…ุน ูƒู„ ุงู„ู†ู‚ุงุท ู‡ุฐู‡ ุจู†ุณู…ูŠู‡ุง
164
00:13:09,810 --> 00:13:16,510
wheel W ุซู„ุงุซุฉ ุชุจุนุง ู„ C ุซู„ุงุซุฉ ุงู„ุขู† ู‡ุฐู‡ complete ุฃู‡
165
00:13:16,510 --> 00:13:19,590
complete ู‡ุฐู‡ ูˆุงุถุญ ุฃู†ู‡ุง complete ู„ุฃู†ู‡ุง ู…ุน ุงู„ูƒู„ ูƒู„
166
00:13:19,590 --> 00:13:26,570
ุงู„ู†ู‚ุงุท ู…ุน ุงู„ูƒู„ ุงู„ุขู† ู‡ุฐู‡ ุงู„ู†ู‚ุทุฉ ู‡ูŠ ุนู†ุฏูŠ ุงู„ู„ูŠ ู‡ูˆ ู…ู†
167
00:13:26,570 --> 00:13:31,630
ุงู„ู†ู‚ุทุฉ ู‡ุฐู‡ ุญุทูŠู†ุง ูˆ ุฑุณู…ู†ุง ู„ูƒู„ ุงู„ู†ู‚ุงุทุŒ ู…ุธุจูˆุทุŸ ู‡ุฐู‡
168
00:13:31,630 --> 00:13:35,050
ุนู…ู„ุช ู„ wheel ู‡ูŠ ู†ูุณู‡ุง ุงู„ู„ูŠ ููˆู‚ ุจุณ ุนู…ู„ู†ุง ู„ู‡ุง ู†ู‚ุทุฉ ูˆ
169
00:13:35,050 --> 00:13:40,390
ู†ู‚ุทุฉ ูˆูˆุฏูŠู†ุง ู„ู‡ุง ุงู„ู„ูŠ ู‡ูŠ ู…ู† ู„ูƒู„ ุงู„ู†ู‚ุงุท ุฎุทูˆุท ุญุณุจ ุชุนุฑูŠู
170
00:13:40,390 --> 00:13:44,370
ุงู„ู„ูŠ ุนุฑูู†ุง ู„ู…ูŠู† ู„ู„ wheel ู‡ู„ ู‡ุฐู‡ completeุŸ ู„ูŠุณ ุดุฑุทุง
171
00:13:44,370 --> 00:13:47,410
ู„ุฃู†ู‡ ููŠุด ุจูŠู† ุงู„ู†ู‚ุทุฉ ู‡ุฐู‡ ู…ุซู„ุง ุงู„ู†ู‚ุทุฉ ู‡ุฐู‡ ุฎุท ู…ุจุงุดุฑ
172
00:13:47,850 --> 00:13:51,270
ู‡ุฐุง ู„ูˆ ุฎุท ู…ู† ู‡ู†ุง ุฅู„ู‰ ู‡ู†ุง ูˆู‡ุฐุง ู…ู† ู‡ู†ุง ุฅู„ู‰ ู‡ู†ุง ู„ุฃู†
173
00:13:51,270 --> 00:13:55,530
ู„ูˆ ูƒุงู† ู‡ู†ุงูƒ ุฎุท ู…ุจุงุดุฑ ุจูŠู†ู‡ู… ู†ุณู…ูŠู‡ complete ู„ูˆ ูƒุงู†
174
00:13:55,530 --> 00:13:59,430
ู‡ู†ุงูƒ ุฎุทูˆุท ู…ู† ุงู„ูƒู„ ุทุจุนุง ุงู„ุขู† ู†ุฃุชูŠ ู„ู‡ุฐู‡ ุงู„ู„ูŠ ู‡ูŠ ุงู„
175
00:13:59,430 --> 00:14:03,850
wheel ุจู†ุฌูŠุจ ุงู„ C3 ูˆ ุจู†ุญุท ู†ู‚ุทุฉ ููŠ ุฏุงุฎู„ู‡ุง ูˆ ุจู†ูˆุตู„
176
00:14:03,850 --> 00:14:08,470
ุจูŠู†ู‡ู… ูƒู„ู‡ู… ุงู„ู„ูŠ ู‡ูŠ ุฅูŠุด ุจูŠู† ุงู„ู†ู‚ุทุฉ ู‡ุฐู‡ ูˆ ุจูŠู† ูƒู„
177
00:14:08,470 --> 00:14:12,030
ุงู„ู†ู‚ุงุท ุงู„ุฃุฎุฑู‰ ุจู†ูˆุตู„ ุฎุทูˆุท ูุจุชุนู…ู„ wheel ู‡ู„ ุงู„ wheel
178
00:14:12,030 --> 00:14:15,090
complete ู„ูŠุณ ุดุฑุทู‹ุง ู„ุฃู† ู‡ูˆ ู…ู† ู‡ู†ุง ุฅู„ู‰ ู‡ู†ุง ู…ุซู„ุง ุฅูŠุด
179
00:14:15,090 --> 00:14:19,810
ู…ุงููŠุด ุฎุท ู‡ูƒุฐุง ุงู„ู„ูŠ ุจุนุฏู‡ุง ุงู„ุขู† ู‡ุฐู‡ ุงู„ู„ูŠ ู‡ูŠ ู…ูŠู† ุงู„ุดูƒู„
180
00:14:19,810 --> 00:14:23,810
ุงู„ุณุฏุงุณูŠ ููŠ ุงู„ุดูƒู„ ุงู„ุณุฏุงุณูŠ ุญุทูŠู†ุง ู†ู‚ุทุฉ ูˆูˆุตู„ู†ุง ุจูŠู†
181
00:14:23,810 --> 00:14:28,090
ุงู„ู†ู‚ุทุฉ ูˆ ุจูŠู† ุจุงู‚ูŠ ุงู„ู†ู‚ุงุท ูุนู…ู„ุช ู„ูŠุด ุจุฑุถู‡ wheel ู‡ุงูŠ
182
00:14:28,090 --> 00:14:32,850
ุดูƒู„ ุงู„ุณุฏุงุณูŠ ุนู†ุฏูŠ ูˆู‡ูŠ ุงู„ู†ู‚ุทุฉ ูˆ ุจุฏูŠ ุงุชูˆุตู„ ู…ู† ุงู„ุดูƒู„
183
00:14:32,850 --> 00:14:37,350
ุงู„ุณุฏุงุณูŠ ู„ูƒู„ ุงู„ู†ู‚ุงุท ุดูˆููˆู‡ุง ู‡ุชุดุชุจู‡ ุชุทู„ุนูˆุด ุชู‚ุจู„ูˆุง ู„ูŠู‡ุง
184
00:14:37,350 --> 00:14:40,310
ุชู‚ูˆู„ูŠู‡ุง ู…ูƒุนุจ ู„ุง ู‡ุฐุง ู…ู‚ุทุจ ููŠ ุงู„ู…ุตู ูˆุทุจุนุง ู‡ูŠ ุจุชุธู‡ุฑ
185
00:14:40,310 --> 00:14:43,790
ู„ูˆ ุงุชู†ุนุงู†ุช ู‡ุชุดูˆูู‡ุง ู…ูƒุนุจ ู„ูˆ ุงุชู†ุนุงู†ุช ููŠ ุตูˆุฑุฉ ุฃุฎุฑู‰
186
00:14:43,790 --> 00:14:47,070
ู‡ุชุดูˆูู‡ุง ู†ู‚ุทุฉ ููŠ ุงู„ุฏุงุฎู„ ูˆ ู…ู† ุงู„ูƒู„ ู…ุด ู…ูˆุถูˆุนู†ุง ู‡ุฐุง ุจุณ
187
00:14:47,070 --> 00:14:51,930
ู„ูƒู† ุนุดุงู† ุงู„ุฎุฏุงุน ุงู„ุจุตุฑูŠ ุทูŠุจ ู‡ุฐู‡ ุงู„ู„ูŠ ู‡ูŠ ู…ุนู†ุงุช ุงู„
188
00:14:51,930 --> 00:14:58,050
wheel ุงู„ุขู† ููŠ ุญุฏ ุงุณู…ู‡ ุจูŠุจุง ุชุฑุงูŠุช ุจูŠุจุง ุจูŠุจุงุฑุชุงูŠุช
189
00:14:58,410 --> 00:15:03,350
graph ุจูŠุจุฑุชุงูŠุช graph ุงู„ู„ูŠ ู‡ูˆ ูŠุนู†ูŠ ุงู„ู€ Graph
190
00:15:03,350 --> 00:15:06,830
ุงู„ุซู†ุงุฆูŠ ุฅูŠุด ุงู„ graph ุงู„ุซู†ุงุฆูŠ ุฎู„ูŠู†ุง ู†ุดูˆู ุฅูŠุด ุจูŠู‚ูˆู„
191
00:15:06,830 --> 00:15:11,030
ุงู„ graph ุงู„ุซู†ุงุฆูŠ a bipartite graph is a graph ู‡ูˆ
192
00:15:11,030 --> 00:15:14,750
ุนุจุงุฑุฉ ุนู† graph whose vertices can be partitioned
193
00:15:14,750 --> 00:15:19,470
into two disjoint sets V1 and V2 ูŠุนู†ูŠ ุงู„ ุจูŠุจุฑุชุงูŠุช
194
00:15:19,470 --> 00:15:23,970
graph ุฃูˆ ุงู„ู„ูŠ ู‡ูˆ ุงู„ graph ุงู„ุซู†ุงุฆูŠ ุจูŠู‚ูˆู„ ู‡ุฐุง ุจุชู‚ุฏุฑ
195
00:15:23,970 --> 00:15:32,640
ุชุนู…ู„ ุงู„ vertices ุฅู„ูŠู‡ ุฌุฒุฆูŠู† V1 ูˆ V2 ู‡ูŠ V1 ูˆู‡ูŠ V2 ุจุณ
196
00:15:32,640 --> 00:15:39,940
ุชุญุช ุดุฑุท ู…ุนูŠู† ูƒู„ Graphs ู…ู…ูƒู† ุชุนู…ู„ู‡ุง V1 ูˆ V2 ุจู‚ุฏุฑ
197
00:15:39,940 --> 00:15:45,220
ุฃุนู…ู„ V1 ูˆ V2 ุจูŠุจู‚ู‰ partition sets ูŠุนู†ูŠ ู‡ุฐูˆู„ ุงู„ู„ูŠ
198
00:15:45,220 --> 00:15:50,540
ุจู†ุณู…ูŠู‡ู… ู‡ู… ุงู„ู„ูŠ ุฌุฒุก ู…ู† ุงู„ set ุงู„ุฃุตู„ูŠ ุชุจุน ุงู„
199
00:15:50,540 --> 00:15:56,440
vertices in such a way ุจุชุฌุฒุฆู‡ุง ุจุทุฑูŠู‚ุฉ ู‡ูŠ V1 ูˆ V2
200
00:15:56,440 --> 00:16:02,840
ุจุชุฌุฒุฆู‡ุง ุจุทุฑูŠู‚ุฉ that every edge point joins a
201
00:16:02,840 --> 00:16:08,070
vertex in V1 ูˆ V2 ูŠุนู†ูŠ ุงู„ุขู† ู„ู…ุง ู†ุงุฎุฏ V1 ูˆููŠู‡ ุงุซู†ูŠู†
202
00:16:08,070 --> 00:16:16,590
ู‡ุชุฌุฒุฆู„ูŠ ุงู„ู„ูŠ ู‡ูŠ ุงู„ vertices ุฅู„ู‰ ุฌุฒุฆูŠู† ุงุจุญุซ ุฃู†ู‡ ูƒู„
203
00:16:16,590 --> 00:16:22,730
edge ููŠ ุงู„ุดูƒู„ ุจุฑุจุท ู†ู‚ุทุฉ ู…ู† ู‡ู†ุง ู…ุน ู†ู‚ุทุฉ ู…ู† ู‡ู†ุง ูƒู„
204
00:16:22,730 --> 00:16:26,590
edge ููŠ ุงู„ุดูƒู„ .. ูƒู„ edge ู…ูˆุฌูˆุฏ ู‡ูŠ edge ุจุฑุจุท ู†ู‚ุทุฉ
205
00:16:26,590 --> 00:16:29,150
ู…ู† ู‡ู†ุง ู…ุน ู†ู‚ุทุฉ ู…ู† ู‡ู†ุง ุงู„ edge ุงู„ุซุงู†ูŠ ู‡ูŠ ุจุฑุจุท ู†ู‚ุทุฉ
206
00:16:29,150 --> 00:16:31,710
ู…ู† ู‡ู†ุง ู…ุน ู†ู‚ุทุฉ ู…ู† ู‡ู†ุง ุงู„ edge ุงู„ุซุงู„ุซ ู…ู† ู†ู‚ุทุฉ ู…ู†
207
00:16:31,710 --> 00:16:33,830
ู‡ู†ุง ู…ุน ู†ู‚ุทุฉ ู…ู† ู‡ู†ุง ุงู„ edge ุงู„ุฑุงุจุน ู…ู† ู†ู‚ุทุฉ ู…ู† ู‡ู†ุง
208
00:16:33,830 --> 00:16:37,390
ู…ุน ู†ู‚ุทุฉ ู…ู† ู‡ู†ุง ูƒู„ ุงู„ุงุชุฌุงู‡ุงุช ุงู„ู„ูŠ ู…ูˆุฌูˆุฏุฉ ุงู„ุฎุทูˆุท
209
00:16:37,390 --> 00:16:42,810
ุจุชูƒูˆู† ูˆุงุตู„ุฉ ุจูŠู† ู†ู‚ุทุฉ ู…ู† ู…ุฌู…ูˆุนุฉ ุงู„ vertices ุงู„ุฃูˆู„ู‰
210
00:16:42,810 --> 00:16:47,770
ูˆู†ู‚ุทุฉ ู…ู† ู…ุฌู…ูˆุนุฉ ุงู„ vertices ุงู„ุซุงู†ูŠุฉ ูŠุนู†ูŠ ุงู„ุขู† ู„ูˆ
211
00:16:47,770 --> 00:16:52,290
ูƒุงู† ุจูŠู† ู‡ุฐู‡ ูˆู‡ุฐู‡ ู„ุง ุจู†ูุนุด ูŠูƒูˆู† ุงู„ู„ูŠ ู‡ูˆ ุฅูŠู‡ ุดู…ุงู„ู‡
212
00:16:52,680 --> 00:16:58,620
ุนู†ุฏูŠ ุงู„ู„ูŠ ู‡ูˆ ุจู…ุณู…ูŠู‡ุด ุนู…ู„ุฉ partition ู„ุฃู†ู‡ ู…ู† ู‡ุงู„ู‡ุงู„
213
00:16:58,620 --> 00:17:02,920
ุจูŠุตูŠุฑ ู‡ุฐุง ุงู„ู†ู‚ุทุฉ ููŠ ู†ูุณ ุงู„ .. ู†ู‚ุทุชูŠู† ููŠ ู†ูุณ ุงู„ V
214
00:17:02,920 --> 00:17:08,420
ูˆุงุญุฏ ู„ุง ู„ุฃู† ูƒู„ ุงู„ุฎุทูˆุท ุจุฏู‡ุง ุชูƒูˆู† ุฌุงูŠุฉ ู…ู† ุงู„
215
00:17:08,420 --> 00:17:13,080
vertices ุงู„ุฃูˆู„ู‰ ู…ุน ุงู„ vertices ุงู„ุซุงู†ูŠุฉ ุนุดุงู† ู‡ูŠูƒ
216
00:17:13,080 --> 00:17:20,280
ุจู†ุณู…ูŠ ู‡ุฐุง bipartite graph ุฃูˆ graph ุซู†ุงุฆูŠ ุงู„ุขู† ู‡ุงูŠ
217
00:17:20,280 --> 00:17:26,820
ูˆุงุญุฏ ุซุงู†ูŠ ุจุฑุถู‡ ุจุจุฑุชุงูŠุฉ graph ุขุฎุฑ ู‡ูŠ ุงู„ V1 ุงู„ูƒุจูŠุฑุฉ
218
00:17:26,820 --> 00:17:31,920
ูŠุนู†ูŠ ุจุชุญุชูˆูŠ ุนู„ู‰ ูƒู„ ุงู„ู„ูŠ ู‡ูŠ ุงู„ vertices ุงู„ุฌุฒุก ุงู„ุฃูˆู„
219
00:17:31,920 --> 00:17:35,980
ูˆู‡ุฐู‡ ุจุชุญุชูˆูŠ ุนู„ู‰ ุงู„ vertices ุงู„ุฌุฒุก ุงู„ุซุงู†ูŠ ู„ุงุญุธ ุฃู†ู‡
220
00:17:35,980 --> 00:17:42,030
ูƒู„ ุฎุท ู…ูˆุฌูˆุฏ ุจุฑุจุท ุจูŠู† ู†ู‚ุทุฉ ุจูŠู† ู‡ุฐู‡ V1 ูˆ V2 ูƒู„ ุฎุท
221
00:17:42,030 --> 00:17:47,670
ู…ูˆุฌูˆุฏ ุจุฑุจุท ุจูŠู† V2 ูˆ V1 ูƒู„ ุฎุท ู…ูˆุฌูˆุฏ ุจูŠู† V1 ูˆ V2 ูˆ
222
00:17:47,670 --> 00:17:54,470
ู‡ูƒุฐุง ู‡ุฐุง ุจู†ุณู…ูŠู‡ู… ุฅุดู…ุงู„ู‡ู… ุฃู…ุซู„ ุนุจุงุฑุฉ ุนู„ู‰ bipartite
223
00:17:54,470 --> 00:17:58,330
graphs ู†ูŠุฌูŠ ู„ุงุฎุฑ ูˆุงุญุฏุฉ ุทุจุนุง ู‡ูŠ ุงู„ุญุงู„ุฉ ู…ู† ุญุงู„ุฉ
224
00:17:58,330 --> 00:18:05,600
ุฑุณู…ู‡ุง ุญุงู„ุฉ ู‡ูŠ ู‡ุฐู‡ ุงู„ู„ูŠ ู‡ูˆ ุงู„ V2 ูˆู‡ูŠ ู‡ุฏู…ูŠู† ุงู„ู€ V1 ู‡ูŠ
225
00:18:05,600 --> 00:18:12,920
ุงู„ู„ูŠ ู‡ู…ุง ุงู„ V1 ูˆ ุงู„ V2 ุงู„ู„ูŠ ุฌุฒุกูŠู† ู„ูŠู‡ ุงู„ู„ูŠ ุฌุฒุกูŠู†
226
00:18:12,920 --> 00:18:18,460
ู„ูŠู‡ ุงู„ู„ูŠ ู‡ูˆ ุงู„ vertices ุงู„ู„ูŠ ุฌุฒุกูŠู† ุงุจุญุซ ุฃู† ูƒู„ ุฎุท
227
00:18:18,460 --> 00:18:24,900
ู…ูˆุฌูˆุฏ ูŠุงุฎุฏ ู…ู† ู†ู‚ุทุฉ ููŠ ุงู„ V1 ุฅู„ู‰ V2 ุฃูˆ ู…ู† V2 ู„ V1 ูˆ
228
00:18:24,900 --> 00:18:29,700
ู‡ูƒุฐุง ุฒูŠ ู…ุง ุฃู†ุชู… ุดุงูŠููŠู† ูู‡ุฏูˆู„ ุฃู…ุซู„ุฉ ุนู„ู‰ bipartite
229
00:18:29,700 --> 00:18:36,590
graphs ุฃูˆ ุฌุฑุงูุงุช ุซู†ุงุฆูŠุฉ ุงู„ู€ Complete bipartite
230
00:18:36,590 --> 00:18:41,310
graph is a bipartite graph in which every vertex
231
00:18:41,310 --> 00:18:46,390
in V1 is joined to every vertex in V2
232
00:18:49,970 --> 00:18:54,290
ุนุจุงุฑุฉ ุนู† ุจูŠุจุฑุชุงูŠุชู‡ graph in which every vertex in
233
00:18:54,290 --> 00:18:58,870
v1 ูƒู„ ุงู„ vertex ููŠ ุงู„ v1 is joined to every vertex
234
00:18:58,870 --> 00:19:03,570
in v2 ู…ุง ู‚ู„ู†ุงุด ุฃู† ูƒู„ ุงู„ vertices ุงู„ู„ูŠ ููŠ ุงู„ v1
235
00:19:03,570 --> 00:19:08,410
ุจุชุชุจุท ู…ุน ุจุนุถ ูˆ ุงู„ v2 ุงู„ู„ูŠ ุจุชุชุจุท ู…ุน ุจุนุถ ู„ุง ู‚ู„ู†ุง ุฃู†
236
00:19:08,410 --> 00:19:13,870
ูƒู„ vertex v1 ุจุชุชุจุท ู…ุน ุฃูŠุด ู…ุน ุงู„ู„ูŠ ููŠ ุงู„ .. ู…ุน
237
00:19:13,870 --> 00:19:19,030
ูˆุงุญุฏ ู…ู† ู…ูŠู† ู…ู† v2 every vertex in v1 is joined to
238
00:19:19,030 --> 00:19:23,280
everyjoin to every ูˆู„ูŠุณ ู…ุน ูˆุงุญุฏ ูู‚ุท to every ูˆุงุญุฏ
239
00:19:23,280 --> 00:19:31,460
ููŠ ุฐูŠ ุงุซู†ูŠู† ุงู„ุขู† ุฎู„ูŠู†ุง ู„ูˆ ุฑุฌุนู†ุง ุงู„ุขู† ู‡ุฐุง ู…ุซู„ุง ู†ุดูˆู
240
00:19:31,460 --> 00:19:35,240
complete ูˆู„ุง ู„ุง ู‡ูŠ ู‡ูŠ ู‡ุฐุง ุจูŠุชุจุท ู…ุน ู‡ุฐุง ูˆุจูŠุชุจุท ู…ุน
241
00:19:35,240 --> 00:19:40,360
ู‡ุฐุง ู„ูƒู† ุจูŠุชุจุทุด ู…ุน ุงู„ู„ูŠ ุจุนูŠุฏ ู‡ุฐุง ุฅุฐุง ู…ุด complete ุทุจ
242
00:19:40,360 --> 00:19:46,630
ุงู„ุขู† ู‡ุฐุง ู‡ูŠ ูˆุจูŠุชุจุท ู…ุน ู‡ุฐุง ูˆุจูŠุชุจุท ู…ุน ู‡ุฐุง ูˆู‡ุฐู‡
243
00:19:46,630 --> 00:19:52,150
ุจุชุชุจุทุด ู…ุน ู…ูŠู†ุŸ ู…ุน ู‡ุฐุง ู„ูˆ ุฑุจุทู†ุงู‡ุง ู…ุน ู‡ุฐุง ูŠุนู†ูŠ ู„ูˆ
244
00:19:52,150 --> 00:19:58,850
ูˆุตู„ู†ุง ู‡ุฐุง ุงู„ุฎุท ู‡ูŠูƒ ูˆูˆุตู„ู†ุง ู‡ุฐุง ุงู„ุฎุท ู‡ูŠูƒ ูˆูˆุตู„ู†ุง ู‡ุฐุง
245
00:19:58,850 --> 00:20:02,670
ุฎุท ูˆุงุตู„ ูุจูŠุตูŠุฑ ุนู†ุฏูŠ ู‡ุฐุง complete ูŠุนู†ูŠ ู…ุชู‰ ุจูŠุตูŠุฑ ู‡ุฐุง
246
00:20:02,670 --> 00:20:07,290
complete ู„ู…ุง ู†ู‡ุงุฏูŠ ู„ุฃู† ู‡ูŠ ูˆุตู„ุช ู…ุน ุญุฏู‡ ูˆูˆุตู„ุช ู…ุน ุญุฏู‡
247
00:20:07,290 --> 00:20:13,030
ูˆู†ูˆุตู„ ู‡ุฐู‡ ู…ุน ุญุฏู‡ ูˆู…ุด ู‡ูŠูƒ ูƒู…ุงู† ูˆู†ูˆุตู„ ู‡ุฐู‡ ู…ุน ุญุฏู‡
248
00:20:13,030 --> 00:20:16,950
ุจูŠุตูŠุฑ ุงู„ graph ุงู„ู„ูŠ ุทู„ุน ุนู†ุฏู‡ ูŠุดู…ู„ู‡ complete ูŠุนู†ูŠ
249
00:20:16,950 --> 00:20:20,490
ุนุดุงู† ูŠูƒูˆู† complete ู‡ุฐุง ุจูŠูƒูˆู† ูƒู„ ูˆุงุญุฏุฉ ู…ู† ู‡ุฏูˆู„
250
00:20:20,490 --> 00:20:26,950
ุงู„ุงุซู†ูŠู† ุจุชุชูˆุตู„ ู…ุน ูƒู„ ูˆุงุญุฏุฉ ู…ู† ุงู„ุซู„ุงุซ ูŠุนู†ูŠ ุจูŠู†ู‡ุง
251
00:20:26,950 --> 00:20:31,070
ูˆุจูŠู† ูƒู„ ุฃุญุฏ ู…ู† ุชู„ุงุชุฉ ุฎุท ูˆุงุถุญ ุฃู†ู†ุง ู†ุณู…ูŠู‡ complete
252
00:20:31,070 --> 00:20:35,200
bipartite graph ุฅุฐุง ุฒูŠ ู…ุง ู‚ู„ู†ุง ุงู„ู€ bipartite graph
253
00:20:35,200 --> 00:20:39,700
ุจูƒูˆู† complete ุฅุฐุง ูƒุงู† ู‡ูˆ bipartite graph ูˆูƒู„
254
00:20:39,700 --> 00:20:46,140
vertex ููŠ ุงู„ู€ V1 is joined to every vertex in V2
255
00:20:46,140 --> 00:20:48,420
ูˆูƒู„ vertex ููŠ ุงู„ู€ V1 is joined to every vertex in
256
00:20:48,420 --> 00:20:53,360
V2 ูˆูƒู„ vertex ููŠ ุงู„ู€ V1 is joined to every vertex
257
00:20:53,360 --> 00:20:53,540
in V2 ูˆูƒู„ vertex ููŠ ุงู„ู€ V1 is joined to every
258
00:20:53,540 --> 00:20:53,600
to every vertex in V2 ูˆูƒู„ vertex ููŠ ุงู„ู€ V1 is
259
00:20:53,600 --> 00:20:53,660
joined to every vertex in V2 ูˆูƒู„ vertex ููŠ ุงู„ู€ V1
260
00:20:53,660 --> 00:20:58,580
vertex ููŠ ุงู„ู€ V1 is joined to every vertex in V2
261
00:20:58,580 --> 00:21:04,130
ูˆูƒู„ vertex ููŠ ุงู„ู€ V1 is ุงู„ู„ูŠ ุจูŠูƒูˆู† ุงู„ู„ูŠ ู‡ูˆ ุงู„ .. ุงู„
262
00:21:04,130 --> 00:21:08,930
.. ุงู„ .. ุงู„ V1 ููŠ M ู…ู† ุงู„ุนู†ุงุตุฑ ูˆ ุงู„ V2 ุจูŠูƒูˆู† M ู…ู†
263
00:21:08,930 --> 00:21:13,890
ุงู„ .. N ู…ู† ุงู„ุนู†ุงุตุฑ ูŠุนู†ูŠ ุนู†ุฏ ุงู„ V1 ุงู„ vertices
264
00:21:13,890 --> 00:21:19,570
ุนุฏุฏู‡ู… M ูˆ ุงู„ V2 ุนุฏุฏู‡ู… N ูˆ ูƒุงู† ู‡ุฐุง bipartite graph
265
00:21:19,570 --> 00:21:24,370
ูˆ ููŠ ู†ูุณ ุงู„ูˆู‚ุช complete ุจูŠูƒูˆู† ุงู„ู„ูŠ ู‡ูˆ ู‡ุงูŠ ุดูƒู„ู‡
266
00:21:24,370 --> 00:21:30,120
ุงุชู†ูŠู† ูˆ ุชู„ุงุชุฉ ุงู„ุงู† ู‡ูŠ ุนู†ุฏูŠ ููˆู‚ ุงุชู†ูŠู† ูˆู‡ุง ุชุญุช
267
00:21:30,120 --> 00:21:33,360
ุงูŠุด ุชู„ุงุชุฉ ุฒูŠ ู…ุง ุนู…ู„ู†ุงู‡ุง ู‚ุจู„ ุดูˆูŠุฉ ู‡ูŠ ุงู„ุงู† ู‡ุฐู‡ ุจุฏู‡ุง
268
00:21:33,360 --> 00:21:39,020
ุชุฑูˆุญ ู„ู„ูƒู„ ู‡ูŠ ุฑุงุญุช ู„ู„ูƒู„ ูˆู‡ุฐู‡ ุจุฑุถู‡ ุฑุงุญุช ู„ุฅูŠุด ู„ู„ูƒู„
269
00:21:39,020 --> 00:21:44,150
ูˆุทุจุนุง ู‡ุฏูˆู„ุฉ ุงูˆุชูˆู…ุงุชูŠูƒ ุฑุงุญู„ู† ู…ูŠู† ู„ุชู†ุชูŠู† ุงู„ู„ูŠ ููˆู‚ ู„ุฃู†
270
00:21:44,150 --> 00:21:47,290
K ุซู„ุงุซุฉ ุซู„ุงุซุฉ ู‡ูŠูƒูˆู† ุนู†ุฏู†ุง ุซู„ุงุซุฉ ู‡ู†ุง ูˆ ุซู„ุงุซุฉ ูˆูŠู†
271
00:21:47,290 --> 00:21:50,730
ููˆู‚ ู„ุฃู† ุงู„ุงุชู†ูŠู† ุงู„ุฃูˆู„ู‰ ุฎู„ูŠู†ุง ู†ุตุทู„ุญ ู…ุน ุจุนุถ ุงู„ู„ูŠ
272
00:21:50,730 --> 00:21:57,230
ุจู†ุฑุณู…ู‡ุง ููˆู‚ ุงู„ุชู„ุงุชุฉ ุงู„ุชุงู†ูŠุฉ ู‡ุฐู‡ ุจู†ุฑุณู…ู‡ุง ุชุญุช ู„ุฃู†
273
00:21:57,230 --> 00:22:00,650
ุชู„ุงุชุฉ ูˆ ุชู„ุงุชุฉ ู‡ูŠ ุชู„ุงุชุฉ ููˆู‚ ูˆ ู‡ูŠ ุชู„ุงุชุฉ ุชุญุช ูˆ ุจู†ูˆุตู„
274
00:22:00,650 --> 00:22:05,150
ู…ู† ูƒู„ ูˆุงุญุฏุฉ ู„ู„ูƒู„ ู…ู…ู†ูˆุน ู†ูˆุตู„ ุจูŠู† ู‡ุฏูˆู„ ุงู„ู„ูŠ ู‡ู†ุง ู…ุน
275
00:22:05,150 --> 00:22:10,110
ุจุนุถ ู„ุฃ ุจูŠุจุทู„ ุงู„ bipartite ุฃุตู„ุง ุงู„ bipartite ุฃู†
276
00:22:10,110 --> 00:22:16,810
ู‡ุฏูˆู„ุฉ ููŠ ุฌู‡ุฉ ูˆ ู‡ุฏูˆู„ุฉ ููŠ ุฌู‡ุฉ ูˆ ุงู„ุฎุทูˆุท ุจูŠู† ู‡ู†ุง ูˆุจุณ
277
00:22:16,810 --> 00:22:23,850
ู…ุงููŠุด ุจูŠู† ุงู„ู„ูŠ ู‡ูˆ ุนู†ุงุตุฑ ุงู„ู„ูŠ ู‡ูŠ ุงู„ V2 ู…ุน ุจุนุถู‡ุง
278
00:22:23,850 --> 00:22:28,590
ุฎุทูˆุท ุจูŠุจุทู„ ุจูŠุจุฑุชุงูŠุฏ ูˆู‡ุฐุง ู†ูุณ ุงู„ุดูŠุก ุทูŠุจ ู„ุฅู† ู†ูŠุฌูŠ
279
00:22:28,590 --> 00:22:32,670
ุชู„ุงุชุฉ ูˆ ุฎู…ุณุฉ ุฅุฐุง ุชู„ุงุชุฉ ุจู†ุฑุณู…ู‡ุง ููˆู‚ ูˆู‡ุฐู‡ ุฎู…ุณุฉ ุชุญุช ูˆ
280
00:22:32,670 --> 00:22:38,950
ุจู†ุทู„ุน ู…ู† ูƒู„ ุชู„ุงุชุฉ ุฎู…ุณ ุฎุทูˆุท ู„ุฎู…ุณ ู†ู‚ุงุท ู…ู† ูƒู„ ุชู„ุงุชุฉ
281
00:22:38,950 --> 00:22:42,630
ุฎู…ุณ ุฎุทูˆุท ู…ู† ูƒู„ ุชู„ุงุชุฉ ุฎู…ุณ ุฎุทูˆุท ูŠุนู†ูŠ ู„ูˆ ุจุฏูƒ ุชูŠุฌูŠ
282
00:22:42,630 --> 00:22:47,210
ุชุญุณุจ ุงู„ุฎุทูˆุท ุงู„ู…ูˆุฌูˆุฏุฉ ู…ู† ู‡ุฐู‡ ุจุชุทู„ุน ู…ู†ู‡ุง ุฎู…ุณ ุฎุทูˆุท
283
00:22:47,210 --> 00:22:51,650
ุฎู…ุณ ุฎุทูˆุท ูˆู…ู† ู‡ุฐู‡ ุฎู…ุณุฉ ูˆู…ู† ู‡ุฐู‡ ุฎู…ุณุฉ ูŠุนู†ูŠ ุฎู…ุณุฉ ุนุดุฑ ุฎุท
284
00:22:52,480 --> 00:22:56,460
ู…ู…ูƒู† ุฃุนุฏ ุฅู† ุงู„ู€ 15 ุงู„ุฎุท ุจุทุฑูŠู‚ุฉ ุชุงู†ูŠุฉ ุฅู† ู‡ุฐู‡ ุงุทู„ุน
285
00:22:56,460 --> 00:23:00,620
ู…ู†ู‡ุง ุชู„ุงุช ุฎุทูˆุท ู„ู„ูŠ ููˆู‚ ุนุดุงู† ูŠุตูŠุฑ complete ูˆู‡ุฐู‡ ุงุทู„ุน
286
00:23:00,620 --> 00:23:03,360
ู…ู†ู‡ุง ุชู„ุงุช ุฎุทูˆุท ู„ู„ูŠ ููˆู‚ ูˆู‡ุฐู‡ ุงุทู„ุน ู…ู†ู‡ุง ุชู„ุงุช ุฎุทูˆุท
287
00:23:03,360 --> 00:23:07,880
ุจูŠุตูŠุฑ ุชู„ุงุช ุฎุทูˆุท ููŠ ุฎู…ุณ ู†ู‚ุงุท ุจุฎู…ุณุฉ ุนุดุฑ ู‡ู†ุง ุฎู…ุณ ู†ู‚ุงุท
288
00:23:07,880 --> 00:23:11,220
ุทุงู„ุนูŠู† ุชู„ุงุช ู†ู‚ุงุท ุทุงู„ุนูŠู† ุงู„ุฎู…ุณ ุฎุทูˆุท ุชู„ุงุชุฉ ููŠ ุฎู…ุณุฉ ุจุฎู…ุณุฉ
289
00:23:11,220 --> 00:23:14,480
ุนุดุฑ ุงุฐุง ุจู‚ุฏุฑ ุฃุนุฏ ุงู„ุฎุทูˆุท ู…ู† ุฃุนู„ู‰ ุฃูˆ ุงู„ุฎุทูˆุท ู…ู†
290
00:23:14,480 --> 00:23:21,730
ุฃุณูู„ ุฒูŠ ู…ุง ูˆุถุญุช ุงู„ุงู† ุงุชู†ูŠู† ูˆ ุณุชุฉ ู‡ูŠ ู†ู‚ุทุฉ ู†ู‚ุทุชูŠู† ูˆู‡ูŠ
291
00:23:21,730 --> 00:23:25,090
ุงู„ู„ูŠ ู‡ูŠ ุณุช ู†ู‚ุทุฉ ุชุญุช ู‡ูŠูƒ ุงู„ุชูุงุฌู†ุฉ ุงู„ุฃูˆู„ู‰ ุจุชุทู„ุน ููˆู‚
292
00:23:25,090 --> 00:23:30,190
ูˆุงู„ุชุงู†ูŠุฉ ุจุชุทู„ุน ุชุญุชู‡ุง ุชุตู„ุญ ุจูŠู†ู‡ุง ูˆุจูŠู† ุจุนุถ ุงู„ุงู† ู‡ุฐู‡
293
00:23:30,190 --> 00:23:34,970
ุงู„ุงุชู†ูŠู† ุงู„ู†ู‚ุทุฉ ุงู„ุฃูˆู„ู‰ ุจุชุทู„ุน ุณุชุฉ ุชู‚ุฑูŠุจุง ุณุช ุฎุทูˆุท ูˆ ู‡ุฏู‰
294
00:23:34,970 --> 00:23:38,650
ุจุชุทู„ุน ุณุช ุฎุทูˆุท ู„ู„ู†ู‚ุงุท ุงู„ู„ูŠ ุชุญุชู‡ุง ูุจุตูŠุฑ ุณุชุฉ ูˆ ุณุชุฉ
295
00:23:38,650 --> 00:23:42,670
ุงุชู†ุงุด ู‡ุฏู‰ ุจุชุทู„ุน ุฎุทูŠู† ูˆ ู‡ุฏู‰ ุฎุทูŠู† ูˆ ู‡ุฏู‰ ุฎุทูŠู† ูƒู„
296
00:23:42,670 --> 00:23:45,670
ูˆุงุญุฏุฉ ุณุช ู†ู‚ุงุท ุจุชุทู„ุน ูƒู„ ูˆุงุญุฏุฉ ุฎุทูŠู† ุจูŠุตูŠุฑ ุณุชุฉ ููŠ
297
00:23:45,670 --> 00:23:49,870
ุงุชู†ูŠู† ุจุงุชู†ุงุด ุฏู‡ ุจู‚ุฏุฑ ุฃุนุฏ ุงู„ู„ูŠ ู‡ูˆ ู…ู† ู‡ู†ุง ุฃูˆ ู…ู† ู‡ู†ุง
298
00:23:49,870 --> 00:23:53,270
ูŠุนู†ูŠ ู‡ุฏูˆู„ุฉ ุจุชุทู„ุนูŠู† ุงุชู†ุงุด ุฎุท ูˆ ู‡ุฏูˆู„ุฉ ุจุชุทู„ุนูŠู† ุงุชู†ุงุด
299
00:23:53,270 --> 00:23:57,100
ุฎุท ูŠุนู†ูŠ ู„ูˆ ุจุฏู†ุง ู†ุญุณุจ ุงู„ degree ู„ู‡ุฏูˆู„ุฉ ุงู„ degree
300
00:23:57,100 --> 00:24:00,980
ู„ู‡ุฏูˆู„ุฉ ุงุชู†ุงุด ูˆ ุงู„ degree ู„ู„ูŠ ููˆู‚ ุจุฑุถู‡ ุงูŠุด ุงุชู†ุงุด
301
00:24:00,980 --> 00:24:06,280
ูŠุนู†ูŠ ู…ุฌู…ูˆุน ุงู„ degree ู…ุฌู…ูˆุน ุงู„ degree ู„ูƒู„ ุงู„ุนู†ุงุตุฑ
302
00:24:06,280 --> 00:24:10,800
ู„ูƒู„ ุงู„ vertices ุงู„ู„ูŠ ู‡ู†ุง ู‡ูŠ ุฃุฑุจุนุฉ ูˆ ุนุดุฑูŠู† ุงู„ู„ูŠ ู‡ูŠ
303
00:24:10,800 --> 00:24:13,920
ุถุนู ุนุฏุฏ ุงู„ุฎุทูˆุท ุฒูŠ ู…ุง ู‚ู„ู†ุง ููŠ ุงู„ู†ุธุฑูŠุฉ ุงู„ู„ูŠ ู‚ู„ู†ุงู‡ุง
304
00:24:13,920 --> 00:24:17,780
ุงู„ู…ุฑุฉ ุงู„ู…ุงุถูŠุฉ ูˆู‡ุฐุง ุงู„ู„ูŠ ู‡ูˆ sum of degree ุงู„ู„ูŠ
305
00:24:17,780 --> 00:24:22,970
ุจุญูƒูŠู‡ ุงู„ุงู† how many edges does K3 ูˆ K6 contains ููŠ
306
00:24:22,970 --> 00:24:27,790
ุงู„ุดุฑุญ ู‚ู„ุชู‡ ู‚ุจู„ ุดูˆูŠุฉ ุจูŠุทู„ุน ู…ู† ุชู„ุงุชุฉ ุณุช ุฎุทูˆุท ูุจุตูŠุฑ
307
00:24:27,790 --> 00:24:33,410
ุนู†ุฏูŠ ูƒู… ุฎุท ุชู„ุงุชุฉ ููŠ ุณุชุฉ ุจุชู…ุงู†ูŠุฉ ุนุดุฑ ู„ุฃู† ุงู„ุณุชุฉ ุจูŠุทู„ุน
308
00:24:33,410 --> 00:24:36,490
ู…ู†ู‡ุง ุชู„ุงุช ุฎุทูˆุท ูƒู„ ูˆุงุญุฏุฉ ุณุชุฉ ููŠ ุชู„ุงุชุฉ ุจุฑุถู‡ ุจุชู…ุงู†ูŠุฉ ุนุดุฑ
309
00:24:36,490 --> 00:24:41,310
ุฅุฐุง ุซู…ุงู†ูŠุฉ ุนุดุฑ ุซู…ุงู†ูŠุฉ ุนุดุฑ ุฎุท ุงู„ู„ูŠ ู‡ูˆ ูˆูƒุฃู†ู‡ ุงู„ degrees
310
00:24:41,310 --> 00:24:45,470
ู„ู‡ุฏูˆู„ุฉ ุงู„ู„ูŠ ู‡ูŠ ูƒู„ ูˆุงุญุฏุฉ ุงู„ degree ุงู„ู„ูŠ ู‡ูŠ ุณุชุฉ ู…ู†
311
00:24:45,470 --> 00:24:50,990
ุงู„ู†ู‚ุงุท ุงู„ุชู„ุงุชุฉ ูุจูƒูˆู† ู…ุฌู…ูˆุน ุงู„ degrees ู„ู„ู†ู‚ุงุท ุงู„ู„ูŠ
312
00:24:50,990 --> 00:24:56,610
ููˆู‚ 18 ุงู„ุงู† ุงู„ 6 ุงู„ู„ูŠ ุชุญุช ุงู„ degree ู„ูƒู„ ูˆุงุญุฏุฉ
313
00:24:56,610 --> 00:24:59,690
ุชู„ุงุชุฉ ู„ุฅู†ู‡ ุจูŠุทู„ุน ู…ู†ู‡ุง ุชู„ุงุช ุฎุทูˆุท ูุจูƒูˆู† ู…ุฌู…ูˆุน ุงู„
314
00:24:59,690 --> 00:25:03,570
degrees ุงู„ู„ูŠ ุชุญุช 18 ูŠุนู†ูŠ ุงู„ู„ูŠ ุชุญุช 18 ูˆ ุงู„ู„ูŠ ููˆู‚ 18
315
00:25:03,570 --> 00:25:08,490
ุจูŠุทู„ุน ุนู† 36 36 ู‡ู†ุง ุถุนู ุนุฏุฏ ุงู„ุฎุทูˆุท ุฒูŠ ู…ุง ุนูƒูŠู†ุง ู‚ุจู„
316
00:25:08,490 --> 00:25:14,120
ุดูˆูŠุฉ ู‡ุฐุง ู‡ูŠ this complete bipartite graph has six
317
00:25:14,120 --> 00:25:17,100
vertices ูŠุนู†ูŠ ู‡ุฐุง ุงู„ู€ Complete bipartite ุงู„ู€ Graph
318
00:25:17,100 --> 00:25:21,860
ุงู„ู„ูŠ ู‚ู„ู†ุง ุนู†ู‡ ุฒูŠ ุงู„ู„ูŠ ุชูˆู‡ ู„ู‡ ุณุชุฉ vertices with
319
00:25:21,860 --> 00:25:25,280
degree ุชู„ุงุชุฉ ูŠุนู†ูŠ ุณุชุฉ vertices with degree ุชู„ุงุชุฉ ูˆ
320
00:25:25,280 --> 00:25:28,660
ุชู„ุงุชุฉ vertices with degree ุณุชุฉ ุฒูŠ ู…ุง ูˆุถุญุช ู‚ุจู„ ูˆ
321
00:25:28,660 --> 00:25:33,220
ุดูˆูŠุฉ ุงู„ุงู† ู…ุฌู…ูˆุน ุงู„ degree ู„ูƒู„ ุงู„ V ุงู„ู„ูŠ ู‡ู…ุง ุงู„ุณุชุฉ
322
00:25:33,220 --> 00:25:38,680
ูˆุงู„ุชู„ุงุชุฉ ุณุชุฉ ูƒู„ ูˆุงุญุฏ degree ุชู„ุงุชุฉ ูˆ ุชู„ุงุชุฉ ูƒู„ ูˆุงุญุฏุฉ
323
00:25:38,680 --> 00:25:44,200
degree ุณุชุฉ ุจุชุทู„ุน ู„ 36 ูŠุนู†ูŠ ุงุชู†ูŠู† ููŠ ุนุฏุฏ ุงู„ุฎุทูˆุท ุงู„ู„ูŠ
324
00:25:44,200 --> 00:25:48,380
ู‡ูˆ ุจูŠูƒูˆู† ุนุฏุฏ ุงู„ุฎุทูˆุท 18 ุฎุท ู„ุฅู† ุงู„ 36 ุฒูŠ ู…ุง ุฃู†ุชูˆ
325
00:25:48,380 --> 00:25:53,600
ุนุงุฑููŠู† ูŠุนู†ูŠ ู…ุถุงุนู ุนุฏุฏ ุงู„ุฎุทูˆุท ู‚ู„ู†ุง ุงุฐุง ุงู„ูƒู„ ุจูŠูƒูˆู†
326
00:25:53,600 --> 00:26:00,410
ุนุฏุฏ ุงู„ุฎุทูˆุท ุนู†ุฏู†ุง 18 ุฎุท So that K36 has 18 edges
327
00:26:00,410 --> 00:26:04,570
ุชู‚ุฑูŠุจุง 18 ุฎุท degree sequence ู†ุนุฑู ุญุงุฌุฉ ุงุณู…ู‡ุง
328
00:26:04,570 --> 00:26:10,800
degree sequence ู†ุดูˆู ุงูŠุด degree sequence ุงู„ุดุนุฑ ุงู„ู„ู‡
329
00:26:10,800 --> 00:26:16,100
ุณู‡ู„ ูŠุนู†ูŠ suppose that D1 ูˆD2 ูˆDn are degree of the
330
00:26:16,100 --> 00:26:18,900
vertices of a graph ูŠุนู†ูŠ ููŠ ุนู†ุฏู†ุง graph ุจูŠุณูŠุฏู‡
331
00:26:18,900 --> 00:26:22,580
graph ุฒูŠ ุงู„ graph ุชุจุนุช ุงู„ู…ุฑุฉ ุงู„ูุงุชุฉ ุนู†ุฏู†ุง graph G
332
00:26:22,580 --> 00:26:27,200
ู‡ุฐุง ุงู„ graph ุฌูŠู†ุง ุญุณุจู†ุง ุงู„ู„ูŠ ู‡ูŠ ููŠู‡ N ู…ู† ุงู„
333
00:26:27,200 --> 00:26:31,020
vertices ุญุณุจู†ุง ุฃูˆู„ ูˆุงุญุฏุฉ ู„ุฌูŠู†ุง ุงู†ู‡ุง degree D1
334
00:26:31,020 --> 00:26:38,320
ุงู„ุชุงู†ูŠุฉ D2 ุงู„ุชู„ุงุชุฉ Dn ุนู†ุฏู…ุง ู†ุฑุชุจู‡ุง ุชู†ุงุฒู„ูŠ D1
335
00:26:38,320 --> 00:26:43,320
ุฃูƒุจุฑ ุณูˆุงุก D2 ุฃูƒุจุฑ ุณูˆุงุก D3 ุฃูƒุจุฑ ุณูˆุงุก DN ู‡ุฐู‡ ุงู„ู€ D1 ูˆD2
336
00:26:43,320 --> 00:26:48,160
ูˆDN ุงู„ู…ุฑุชุจุฉ ุงู„ู„ูŠ ู‡ูŠ ุจุดูƒู„ ุชู†ุงุฒู„ูŠ
337
00:26:48,980 --> 00:26:55,540
ุงู„ู„ูŠ ู‡ูŠ ุทุจุนุง ุฏูŠ ูˆุงุญุฏ ุชู…ุซู„ ุงู„ degree ู„ ุงู„ู„ูŠ ู‡ูˆ ู†ู‚ุทุฉ
338
00:26:55,540 --> 00:26:58,520
ุฃูˆู„ู‰ ู‡ุฐู‡ ุงู„ degree ู„ู„ุชุงู†ูŠุฉ ู‡ุฐู‡ ุงู„ degree ู„ู„ุฃุฎูŠุฑุฉ
339
00:26:58,520 --> 00:27:03,760
ู„ู…ุง ู†ุฑุชุจู‡ ุชู†ุงุฒู„ูŠ ุฒูŠ ู‡ูŠูƒ ุจู†ุณู…ูŠู‡ degree
340
00:27:03,760 --> 00:27:08,220
sequence of G ุงู„ู„ูŠ ู‡ูŠ degree sequence ู„ู…ูŠู† ู„ู„ G ููŠ
341
00:27:08,220 --> 00:27:11,620
ุงู„ูˆุงู‚ุน degree sequence ู„ู„ G ู„ุฃ ู‡ูŠ ููŠ ุงู„ูˆุงู‚ุน ุงู„
342
00:27:11,620 --> 00:27:16,530
degree sequence ู„ู„ vertices ุชุจุนุงุช ุงู„ G ู‡ุฐุง ุงุตุทู„ุงุญุง
343
00:27:16,530 --> 00:27:19,930
ู…ุน ุจุนุถ ุนุดุงู† ู„ู…ุง ู†ุญูƒูŠ ุนู† ุงู„ degree sequence of G
344
00:27:19,930 --> 00:27:26,130
ู†ูƒูˆู† ูุงู‡ู…ูŠู† ุงู†ู‡ ุจู‚ุตุฏ ุงู†ู‡ ุจู†ุฌูŠุจ ุงู„ู„ูŠ ู‡ูˆ ุงู„ degree
345
00:27:26,130 --> 00:27:31,910
ู„ูƒู„ ู„ูƒู„ ู†ู‚ุทุฉ ู…ู† ุงู„ู†ู‚ุงุท ูˆ ุจุนุฏูŠู† ุจู†ุฑุชุจู‡ุง ุชุตุงุนุฏูŠ ุชู†ุงุฒู„ูŠ
346
00:27:31,910 --> 00:27:37,050
ุฏู‡ ู†ุดูˆู ู‡ุงูŠ ุนู†ุฏูŠ ู…ุซู„ุง V1 V2 ู‡ุงูŠ ุงู„ุฎุทูˆุท ุงู„ู„ูŠ ุจูŠู†ู‡ู…
347
00:27:37,050 --> 00:27:43,440
ุงู„ degree ู„ู„ V1 ู‡ูŠ 1 2 ุงู„ degree ู„ู„ V2 ู‡ูŠ ูˆุงุญุฏ
348
00:27:43,440 --> 00:27:51,040
ุงุชู†ูŠู† ุชู„ุงุชุฉ ุตุญ ุงู„ degree ู„ู„ V3 ู‡ูŠ ูˆุงุญุฏ ุงุชู†ูŠู† ูˆ ู‡ุฐุง
349
00:27:51,040 --> 00:27:55,240
ุฒูŠ ู…ุง .. ุฏู‡ ูุงูƒุฑูŠู† ุจู†ุญุณุจ ุงูŠุด ุงุชู†ูŠู† ู‡ูŠ ุฃุฑุจุนุฉ ูˆ ู‡ุฐู‡
350
00:27:55,240 --> 00:27:59,260
ุงู„ degree ุงู„ู„ูŠ ู‡ูŠ ุงูŠุด ูˆุงุญุฏ ุงุฐุง ููŠ ุนู†ุฏูŠ .. ู‡ูŠ ููŠ
351
00:27:59,260 --> 00:28:04,320
ุนู†ุฏูŠ ุฃุฑุจุนุฉ ู‡ุฐู‡ ุงู„ V3 ุฃุฑุจุนุฉ ุงู„ degree ู„ู‡ุง ูˆ V2
352
00:28:04,320 --> 00:28:11,620
ุงุชู†ูŠู† V2 ุชู„ุงุชุฉ ุงุณู ู‡ูŠ ูˆุงุญุฏ ู‡ูŠ ุงุชู†ูŠู† ู‡ูŠ ุชู„ุงุชุฉ ู‡ูŠ ุงุฐุง
353
00:28:11,620 --> 00:28:17,620
V3 V2 ุงู„ degree degree V3 degree V2 ุฃุฑุจุนุฉ ุชู„ุงุชุฉ
354
00:28:17,620 --> 00:28:21,540
ุจุนุฏูŠู† ุงู„ุฃุฌู„ ู…ู† ู‡ู†ุง ุงู„ degree ู„ V1 2 ุจุนุฏูŠู† ุงู„ degree
355
00:28:21,540 --> 00:28:26,200
ู„ V4 ุงู„ู„ูŠ ู‡ูˆ ูˆุงุญุฏ ูŠุนู†ูŠ ุจูŠุตูŠุฑ ุนู†ุฏูŠ the degree
356
00:28:26,200 --> 00:28:29,600
sequence of the pseudograph ู‡ุฐุง ุงู„ู„ูŠ ุฃู…ุงู…ู†ุง is
357
00:28:29,600 --> 00:28:38,600
degree V3 ุงู„ู„ูŠ ู‡ูŠ ุฃุฑุจุนุฉ degree V2 ุงู„ู„ูŠ ู‡ูŠ ุชู„ุงุชุฉ
358
00:28:38,600 --> 00:28:45,200
degree V1 ุงู„ุชูŠ ู‡ูŠ ูˆุงุญุฏ ุงุชู†ูŠู† degree V4 ุงู„ุชูŠ ู‡ูŠ
359
00:28:45,200 --> 00:28:50,560
ูˆุงุญุฏ ุงุฐุง ู‡ุฐู‡ ุงู„ู„ูŠ ู‡ูŠ ู…ุซุงู„ ุนู„ู‰ ุงู„ู€ sequence degree
360
00:28:50,560 --> 00:28:55,960
ุฃูˆ ุงู„ู€ degree sequence of this pseudograph ุงู„ุฃู…ุงู…ูŠ
361
00:28:55,960 --> 00:29:06,080
ุงู„ุขู† how many degree does a graph have if its
362
00:29:06,080 --> 00:29:09,920
degree sequence is ุฎู…ุณุฉุŒ ุงุชู†ูŠู†ุŒ ุงุชู†ูŠู†ุŒ ุงุชู†ูŠู†ุŒ
363
00:29:09,920 --> 00:29:15,300
ุงุชู†ูŠู†ุŒ ูˆุงุญุฏ draw such a graph ุจู‚ูˆู„ ู„ูŠู‡ ุงู„ุขู† ุฌุฏุงุด ุงู„
364
00:29:15,300 --> 00:29:19,160
degree ุงู„ู„ูŠ ู‡ูˆ ุฌุฏุงุด ุงู„ู„ูŠ ู‡ูˆ how many edges ุฌุฏุงุด
365
00:29:19,160 --> 00:29:24,360
ุนุฏุฏ ุงู„ edges ุงู„ู„ูŠ ููŠ ุงู„ .. ุงู„ู„ูŠ .. ุงู„ู„ูŠ ููŠ ุงู„ุฌุฑุงู
366
00:29:24,360 --> 00:29:28,160
ุงู„ู„ูŠ ุนู†ุฏูŠ ุงู„ู„ูŠ ุงู„ degree ู„ูƒู„ู‡ ุงู„ู„ูŠ ุงู„ degree
367
00:29:28,160 --> 00:29:33,840
sequence ุงู„ู„ูŠ ู‡ูˆ ู‡ูŠ how many edges of a graph ูƒู…
368
00:29:33,840 --> 00:29:39,200
ุฎุท ููŠ ููŠ ุงู„ุฌุฑุงู ุฅุฐุง ูƒุงู†ุช ุงู„ degree sequence ูŠุนู†ูŠ ุงู„
369
00:29:39,200 --> 00:29:44,820
degree sequence ุดูƒู„ู‡ุง ุจุฏู‡ุง ู‡ูŠ ุชุฌุนู„ู†ุง ู†ุนุฑู ู†ุฑุณู… ุงู„
370
00:29:44,820 --> 00:29:50,220
graph ู‡ูŠ ุงู„ู„ูŠ ุจุชุฌุนู„ู†ุง ู†ุนุฑู ุฌุฏุงุด ุงู„ุฎุทูˆุท ุงู„ู„ูŠ ููŠู‡ุง
371
00:29:50,220 --> 00:29:56,100
ุงู„ู„ูŠ ุฃู†ุง ู…ู‚ูˆู„ is ุฎู…ุณุฉ ูˆ ุงุชู†ูŠู† ูˆ ุงุชู†ูŠู† ูˆ ุงุชู†ูŠู† ูˆ
372
00:29:56,100 --> 00:30:01,300
ุงุชู†ูŠู† ูˆ ูˆุงุญุฏ ุฃูˆู„ ุญุงุฌุฉ ุจุฏูŠ ุจุชุทู„ุน ู‡ุฐูˆู„ ุฃูƒุจุฑ ู†ู‚ุทุฉ ู‡ุฐู‡
373
00:30:01,300 --> 00:30:05,200
ูƒู„ ูˆุงุญุฏุฉ ู†ู‚ุทุฉ ู…ู† ุงู„ู†ู‚ุงุท ู„ุฃู†ู‡ุง ุจุชู…ุซู„ degree ู„ู„ู†ู‚ุงุท
374
00:30:05,200 --> 00:30:10,920
ู‡ุฐู‡ ู†ู‚ุทุฉ ู†ู‚ุทุชูŠู† ุชู„ุงุชุฉ ุฃุฑุจุนุฉ ุฎู…ุณุฉ ุณุชุฉ ุฅุฐุง ุณุช ู†ู‚ุงุท
375
00:30:10,920 --> 00:30:16,280
ู„ู…ุง ุขุชูŠ ุฃุทู„ุน ู„ degree ุงู„ู†ู‚ุทุฉ ู‡ุฐู‡ ุงู„ุฃูˆู„ู‰ ุจู‚ูˆู„ ุณุชุฉ
376
00:30:16,280 --> 00:30:22,500
ุทุงู„ุน ู…ู†ู‡ุง ุงู„ู„ูŠ ู‡ูŠ degree ู„ู‡ุง ุฎู…ุณุฉ ู…ุงุดูŠ ุฅุฐุง ุฑุงูŠุญุฉ
377
00:30:22,500 --> 00:30:27,080
ู„ูˆุงุญุฏ ู„ุงุชู†ูŠู† ู„ุชู„ุงุชุฉ ู„ุงุฑุจุนุฉ ู„ุฎู…ุณุฉ ุฅุฐุง ููŠ ุฅู„ูŠู‡ุง ุฅูŠู‡
378
00:30:27,080 --> 00:30:32,160
ุดู…ุงู„ู‡ุง ุทุงู„ุน ู…ู†ู‡ุง ุฎู…ุณ ุฎุทูˆุท ุงู„ุชู†ูŠู† ุทุงู„ุน ู…ู†ู‡ุง ุฎุทูŠู†
379
00:30:33,030 --> 00:30:37,010
ุงู„ุชู†ูŠู† ุฎุทูŠู† .. ุงู„ุชู†ูŠู† ุฎุทูŠู† .. ุงู„ุชู†ูŠู† ุฎุทูŠู† ..
380
00:30:37,010 --> 00:30:42,650
ุงู„ูˆุงุญุฏ ุฎุทูŠู† .. ุฅุฐุง ู„ู…ุง ุฃุญุณุจ ุงู„ degree .. ุงู„ degree
381
00:30:42,650 --> 00:30:48,310
ุงู„ุฃูˆู„ู‰ ุฎู…ุณุฉ ุฌุฏู‘ุงุด ุงู„ุฃูˆู„ู‰ ุฎู…ุณุฉ ูˆุงู„ุซุงู†ูŠุฉ ุงุซู†ูŠู†
382
00:30:48,310 --> 00:30:50,630
ูˆุงู„ุซุงู†ูŠุฉ ุงุซู†ูŠู† ูˆุงู„ุซุงู†ูŠุฉ ุงุซู†ูŠู† ูˆุงู„ุซุงู†ูŠุฉ ุงุซู†ูŠู† ูˆุงุญุฏุฉ
383
00:30:50,630 --> 00:30:54,390
ู‡ุฐุง ู…ุฌู…ูˆุน ุงู„ degrees ู„ู…ูŠู†ุŸ ู„ู„ู†ู‚ุงุท ุงู„ู„ูŠ ู…ูˆุฌูˆุฏุฉ ู„ุฃู†
384
00:30:54,390 --> 00:30:57,530
ู‡ูŠ ุงู„ sequence ู„ู„ degrees ู„ู„ู†ู‚ุงุท ูƒู„ู‡ุง ููƒู…ุง
385
00:30:57,530 --> 00:31:01,090
ุฃุนุทูŠู†ูŠู‡ุง ุฅุฐู† ุฃุฑุจุนุชุงุด ูˆุงุญู†ุง ุงุชูุงุฌุฃู†ุง ุงู„ุฃุฑุจุนุชุงุด ุฃูŠุด
386
00:31:01,090 --> 00:31:05,410
ุจูŠุณุงูˆูŠ ุฅู† ุงุซู†ูŠู† ุถุนู ุงู„ุฎุทูˆุท ู‡ุฐู‡ ู†ุธุฑูŠุฉ ุฎุฏู†ุงู‡ุง ุงู„ู…ุฑุฉ
387
00:31:05,410 --> 00:31:08,770
ุงู„ู…ุงุถูŠุฉ ุงุซู†ูŠู† ุถุนู ุงู„ุฎุทูˆุท ูŠุนู†ูŠ ุนุฏุฏ ุงู„ุฎุทูˆุท ุฃูŠุด
388
00:31:08,770 --> 00:31:12,810
ุจูŠุณุงูˆูŠ ุณุจุนุฉ ุฅุฐุง ุงู„ edges ุงู„ู„ูŠ ู…ูˆุฌูˆุฏุฉ ู‡ูŠ ุนุจุงุฑุฉ ุนู†
389
00:31:12,810 --> 00:31:18,470
ุณุจุนุฉ ู…ุงุดูŠ ุณุจุนุฉ ุงู„ุขู† ูƒูŠู ุจุชุฏุฑุณู…ู‡ุง ุงู„ุณุจุนุฉ ุงู„ุขู† ุจุงุฌูŠ
390
00:31:18,470 --> 00:31:22,150
ู„ู„ู†ู‚ุทุฉ ุงู„ู„ูŠ ู‡ูŠ ุงู„ู„ูŠ .. ุงู„ู„ูŠ ู‡ูŠ ุนู†ุฏู‡ ุณุช ู†ู‚ุงุท ุจุญุท
391
00:31:22,150 --> 00:31:26,570
ูˆุงุญุฏุฉ ุงุซู†ุชูŠู† ุซู„ุงุซ ุฃุฑุจุน ุฎู…ุณุฉ ูˆู‡ูŠ ุณุช ู‡ูŠ ุณุช ู†ู‚ุงุท
392
00:31:26,570 --> 00:31:30,370
ู…ุงุดูŠ ู„ูŠุด ุญุทูŠุชู‡ุง ู‡ู†ุง ุฏูŠ ูˆู…ุงุญุทูŠุชู‡ุงุด ู‡ู†ุงุŸ ู„ุฃู† ุฃู†ุง
393
00:31:30,370 --> 00:31:33,210
ุนุงุฑู ู‡ุฐุง ุฅู† ููŠ ู†ู‚ุทุฉ ู…ู† ุงู„ู†ู‚ุงุท ุงู„ู„ูŠ ู‡ูŠ ุทุงู„ุน ู…ู†ู‡ุง
394
00:31:33,210 --> 00:31:38,490
ุฌุฏู‘ุงุด ุฎู…ุณ ุฎุทูˆุท ูŠุนู†ูŠ ุทุงู„ุน ู…ู†ู‡ุง ุฏูŠ ุฎุท ู‡ู†ุง ูˆู‡ู†ุง ุฎุท ูˆ
395
00:31:38,490 --> 00:31:43,520
ู‡ู†ุง ุฎุท ูˆู‡ู†ุง ุฎุท ูŠุนู†ูŠ ุทุงู„ุน ู„ู‡ุง ู„ูƒู„ ุฎุทูˆุท ูู‡ู†ุง ุฃุณู‡ู„ ููŠ
396
00:31:43,520 --> 00:31:47,560
ุงู„ุฑุณู… ุจุณ ุนุดุงู† ุณู‡ูˆู„ุฉ ุงู„ุฑุณู… ูŠุนู†ูŠ ูˆุงุญุฏ ุซุงู†ูŠ ู…ู…ูƒู† ูŠุญุท
397
00:31:47,560 --> 00:31:51,960
ู‡ู†ุง ู‡ู†ุง ู…ู…ูƒู† ูŠุญุทู‡ุง ูˆูŠู‚ุนุฏ ูŠุฑุณู… ูˆูŠุตู„ ุจูŠู†ู‡ู… ุจู†ูุน ู‡ู†ุง
398
00:31:51,960 --> 00:31:55,580
ู…ู…ูƒู† ูŠุญุทู‡ุง ู‡ู†ุง ู…ู…ูƒู† ูŠุญุทู‡ุง ูŠุนู†ูŠ ู…ู…ูƒู† ูŠูƒูˆู† ุงู„ุฑุณู… ุตุญ
399
00:31:55,580 --> 00:32:00,880
ู„ูƒู† ุดูƒู„ู‡ุง ู…ุฎุชู„ู ู…ู† ูˆุงุญุฏ ู„ูˆุงุญุฏ ุจุณ ุจูŠูƒูˆู† ุฃูŠุด ุงู„ุตุญ ุฅู†
400
00:32:00,880 --> 00:32:05,510
ุงู„ู†ู‡ุงุฑุฏุฉ ุทุงู„ุน ู„ู‡ุง ุฎู…ุณ ุฎุทูˆุท ู‡ุงูŠูŠู† ู‡ุงูŠ ุงู„ุฎู…ุณุฉ ุงู„ุขู†
401
00:32:05,510 --> 00:32:09,750
ุงู„ู†ู‚ุทุฉ ุงู„ุซุงู†ูŠุฉ ุงู„ุชุงู†ูŠุงุช ูƒู„ู‡ู… ูˆุงุญุฏุฉ ุงุซู†ุชูŠู† ุซู„ุงุซุฉ
402
00:32:09,750 --> 00:32:13,690
ุฃุฑุจุน ูƒู„ู‡ู… ุดู…ุงู„ ููŠู† ุฎุทูŠู† ุฎุทูŠู† ุฎุทูŠู† ูŠุนู†ูŠ ู‡ุฐู‡ ุงู„ุขู†
403
00:32:13,690 --> 00:32:17,650
ุจุชุทู„ุน ุจูŠู†ู‡ุง ุฎุทูŠู† ู‡ูŠุฏูŠ ู…ุญุฏุฏ ูˆู‡ุฐู‡ ุฎุท ู‡ูŠ ู‡ุฐู‡ ูˆู‡ุฐู‡ ุฎุท
404
00:32:17,650 --> 00:32:21,590
ูˆู‡ุฐู‡ ูˆู‡ุฐู‡ ุฎุท ูˆู‡ุฐู‡ ูˆู‡ุฐู‡ ุฎุท ูˆุจู†ุฎู„ูŠ ูˆุงุญุฏุฉ ุจุณ ุจูŠุทู„ุน
405
00:32:21,590 --> 00:32:24,550
ู…ู†ู‡ุง ุฎุท ุงู„ู„ูŠ ู‡ูˆ ุทุงู„ุน ุนู„ู…ูŠุง ู„ู‡ุฐุง ุงู„ู†ู‚ุทุฉ ุฎุงุตุฉ ุนู†ู‡ุง
406
00:32:24,550 --> 00:32:28,730
ุนุดุงู† ู†ุณูŠู†ุง ุงู„ุฎู…ุณุฉ ุฏูˆู„ุงุฑ ูู‡ุฐุง ุจูŠูƒูˆู† ุงู„ู„ูŠ ู‡ูˆ ุฑุณู…ู†ุง ู„
407
00:32:28,730 --> 00:32:34,110
graph ู…ู† ูˆุนุฑูู†ุง ุฌุฏู‘ุงุด ุนุฏุฏ ุงู„ุฎุทูˆุท ู…ู† ุฎู„ุงู„ ุงู„ู„ูŠ ู‡ูˆ
408
00:32:34,110 --> 00:32:40,300
ู…ุนุฑูุฉ ุงู„ degree ุณูŠูƒูˆุงู†ุณ ู„ู„ู€ vertices ุชุจุนุงุช ุงู„ graph
409
00:32:40,300 --> 00:32:45,660
ูˆู‡ูŠ ูƒู…ุง ู†ูƒูˆู† ุงุญู†ุง ุฎู„ุตู†ุง ุงู„ู…ุญุงุถุฑุฉ ุฑู‚ู… 11 ูˆู‡ูŠ ุนู†ุฏูƒู…
410
00:32:45,660 --> 00:32:50,460
ุงู„ homework ุงู„ู…ุทู„ูˆุจ ุชุญู„ูˆ ูˆุชุณู„ู…ูˆู†ูŠู‡ุง ูƒุงู„ุนุงุฏุฉ ุฅู†
411
00:32:50,460 --> 00:32:53,700
ุดุงุก ุงู„ู„ู‡ ูˆุฅู„ู‰ ู„ู‚ุงุก ุขุฎุฑ ุงู„ุณู„ุงู… ุนู„ูŠูƒู… ูˆุฑุญู…ุฉ ุงู„ู„ู‡
412
00:32:53,700 --> 00:32:54,280
ูˆุจุฑูƒุงุชู‡