Graph (discrete mathematics) | Wikipedia audio article
Channel: wikipedia tts
Date: 11/01/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)


00:01:40 1 Definitions
00:02:01 1.1 Graph
00:04:12 1.2 Adjacency relation
00:04:41 2 Types of graphs
00:04:50 2.1 Distinction in terms of the main definition
00:05:29 2.1.1 Undirected graph
00:06:10 2.1.2 Directed graph
00:06:28 2.1.3 Oriented graph
00:07:41 2.1.4 Mixed graph
00:08:05 2.1.5 Multigraph
00:08:12 2.1.6 Simple graph
00:08:22 2.1.7 Quiver
00:08:50 2.1.8 Weighted graph
00:08:59 2.1.9 Half-edges, loose edges
00:09:20 2.2 Important classes of graph
00:10:24 2.2.1 Regular graph
00:11:06 2.2.2 Complete graph
00:11:53 2.2.3 Finite graph
00:12:38 2.2.4 Connected graph
00:13:02 2.2.5 Bipartite graph
00:13:12 2.2.6 Path graph
00:13:38 2.2.7 Planar graph
00:13:58 2.2.8 Cycle graph
00:14:29 2.2.9 Tree
00:16:11 2.2.10 Advanced classes
00:16:55 3 Properties of graphs
00:17:17 4 Examples
00:17:39 5 Graph operations
00:17:48 6 Generalizations
00:18:01 7 See also
00:18:10 8 Notes
00:18:46 9 References
00:19:07 10 Further reading
00:19:45 11 External links
00:21:57 Examples
00:23:29 Graph operations
00:24:30 Generalizations
00:25:45 See also



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SUMMARY
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In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called an arc or line). Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.
The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person A can shake hands with a person B only if B also shakes hands with A. In contrast, if any edge from a person A to a person B corresponds to A's admiring B, then this graph is directed, because admiration is not necessarily reciprocated. The former type of graph is called an undirected graph and the edges are called undirected edges while the latter type of graph is called a directed graph and the edges are called directed edges.
Graphs are the basic subject studied by graph theory. The word "graph" was first used in this sense by James Joseph Sylvester in 1878.