Talk:Degree (graph theory)

message: Someone needs to fix the graph with the caption "An undirected graph with leaf nodes 4, 5, 6, 7, 10, 11, and 12". Node 10 is depicted as "18" in the graph. Figs 19:57, 14 March 2007 (UTC)
replies: text: No its not. The zero just got a dot in it that makes i look like 18 if you dont look carefully. :)  —Preceding unsigned comment added by 129.16.25.17 (talk) 11:23, 13 March 2008 (UTC)
thread_title: Image:Depth-first-tree

message: I'm boldly redirecting Degree sum formula (present version) to this article, since it has been a stub for two years now and its content is already here. Melchoir (talk) 05:03, 22 March 2008 (UTC)
thread_title: Degree sum formula

message: 1. Degree sequence.
2. Degree sequence of graphs and hypergraphs.
Degree sequence is itself pretty big.
The Graph (mathematics) covers the basic definitions of graphs.
--Tangi-tamma (talk) 13:41, 20 April 2008 (UTC)
replies: text: Oppose. "Degree sequence" is already re-directed here. "Degree sequence of graphs and hypergraphs" is not likely to be a search term. Leave title as is. Gandalf61 (talk) 16:48, 20 April 2008 (UTC)

text: This article is not only about degree sequences. Renaming it to "Degree sequence" would suggest that all degree-related data in a graph can be derived from its degree sequence, which is not the case. If "Degree (graph theory)" is really that unpalatable, then an equivalent title without parentheses would be "Degree of a vertex". Melchoir (talk) 02:16, 22 April 2008 (UTC)

text: Degree is a very important concept in graph theory, and lots of articles link here.  We need to keep this article.  Degree sequences may fit in as a subsection (my preference), or perhaps as an article on their own. Radagast3 (talk) 06:23, 1 May 2008 (UTC)
thread_title: I recommend changing the title "Degree (Graph theory)" to one of the followings

message: The para needs editing using the math symbols.
--Tangi-tamma (talk) 20:29, 20 April 2008 (UTC)
thread_title: Undirected graph

message: I removed the following new section of text from the article:
:Let P be any property that goes with a graph. Crispin St. J. A. Nash-Williams called a graphic degree sequence a Potentially P if the graphic degree sequence has at least one realization with property P. He called a Forcibly P  if every realization of the graphic degree sequence has that property P. These concepts set forth a series of open research problems in degree sequence.
:The sequence (13, 12, 11, 10, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2) on 14 vertices is an example of a forcibly  Hamiltonian graphic sequence. The sequence (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2) is an example of a potentially  Hamiltonian graphic sequence. The problem of characterization of forcibly  Hamiltonian graphic degree sequences is a classical open problem.
Removed because:
1) It is badly written and barely coherent.
2) As it appears to be talking about an open problem concerning Hamiltonian graphs, it does not belong in this article anyway. Gandalf61 (talk) 08:21, 21 April 2008 (UTC)
replies: text: I don't see the point of that sentence. The sequence (2, 2, 2) is also the degree sequence of a Hamiltonian graph, but who cares? Melchoir (talk) 02:30, 22 April 2008 (UTC)

text: If you mean my edits, I could cite them to some random book found on Google, as could any reader very quickly. As long as the material isn't being challenged, I'd prefer if someone took the time to find a really good reference, preferably a review article. Melchoir (talk) 02:33, 22 April 2008 (UTC)
thread_title:  Removed section 

message: It is better to remove the portion when someone plays with rm. Since I do not have the citation, I cannot give it at this time. I will place the section here for future use if someone is able to get the reference.
The verification is as simple as understnding the simple graphs. Sosmeone could verify it easily. I cannot post the code that gets that number stated there.
Here is the piece.
Let p be any positive even integer. Let P(p) denote the set of all partitions of p . A partition  in P(p) is graphical if it is the degree sequence of some simple graph. For example, (5,4, 4, 2, 2, 1) is not graphical. Let G(p) denote the set of all graphical partitions of p.
The computation of |G(p)| can be done in O(p4). For p=50, |G(p)| = 76104 and |P(p)| = 204,226. Thus the ratio 
|G(p)| to |P(p)| tends to 0.25 as  p tends infinity.
Also notice that some said about Erdos paper, but he/she forgot to cite. How about this?
--Tangi-tamma (talk) 13:15, 21 April 2008 (UTC)
replies: text: If you mean my edits, I could cite them to some random book found on Google, as could any reader very quickly. As long as the material isn't being challenged, I'd prefer if someone took the time to find a really good reference, preferably a review article. Melchoir (talk) 02:33, 22 April 2008 (UTC)
thread_title:  '''0.25 '''

message: I changed the appearance of loops in the header.  Previously it claimed that "the number of edges incident to the vertex" implies that loops contribute 2, but that is not correct as a loop is only one edge.  To explain this better, can someone please modify the figure to add a loop on vertex 1?  (I can't edit SVG files.)  Then we can have an extra sentence something like "The degree of vertex 1 in the figure is 3, since the loop contributes 2."  McKay (talk) 01:18, 10 April 2009 (UTC)
thread_title:  Loops 

message: This article misuses the term "multigraph" (or at least uses it in a way that will mislead many readers). Customarily, a multigraph may have more than one connection between the same two vertices. This is orthogonal to whether self-loops are allowed. 
This article even shows an illustration, labelled a "multigraph", which only has self-loops, but not multi-edges. It also makes statements that are valid only if self-loops are allowed, but invalid for self-loop-free graphs with multi-edges.  — Preceding unsigned comment added by 2A02:2454:8920:8700:997:DE8B:4887:1FA8 (talk) 14:00, 6 July 2020 (UTC)
replies: text: You are right. Corrected the caption. You could have done this yourself.--Bill Cherowitzo  (talk) 19:05, 6 July 2020 (UTC)
thread_title:  Article misuses "multigraph"