Vertex-transitive graph (552 bytes)
1: ...-transitive [[Graph (mathematics)|graph]]''' is a graph ''G'' such that, given any two vertices v<sub>1</...
9: In other words, a graph is vertex-transitive if its automorphism group acts [[Group...
11: Every vertex-transitive graph is [[Regular graph|regular]]
14: * [[Edge-transitive graph]]
18: [[Category:Graphs]]

Graph theory (9461 bytes)
1: ...]]s (or Arcs) which can be directed. Typically, a graph is designed as a set of dots (the vertices) conne...
4: <tr><td>''A graph with 6 vertices and 7 edges.''</td></tr></table>
6: ...'B''. The development of [[algorithm]]s to handle graphs is therefore of major interest in [[computer sci...
8: ...y called a [[digraph]]. Within graph theory, a digraph with weighted edges is called a [[network (mathem...
10: ...network is much looser, and may often be a simple graph.

Snark (graph theory) (1145 bytes)
1: In [[graph theory]], a '''snark''' is a
2: ...eory#Connectivity|connected, bridgeless]] [[cubic graph]] with [[chromatic index]] equal to four.
4: In other words, it is a graph in which every node has three branches, and the e...
10: ...ntains the [[Petersen graph]] as a [[minor (graph theory)|minor]].
13: *[[Petersen graph]] (10 vertices; 1891)

Distance (graph theory) (1876 bytes)
1: ...tween two [[vertex_(graph theory)|vertices]] in a graph.
5: ...ry)|vertices]] and ''E'' the set of [[edge_(graph theory)|edges]] then the '''distance''' between two vert...
8: The '''eccentricity''' of a vertex ''v'' is
11: The '''diameter''' of the graph is defined as
14: A '''peripheral vertex''' for ''G'' is a vertex ''v'' with

Degree (graph theory) (1360 bytes)
1: ...h theory)|incident]] to ''v'' (with [[loop (graph theory)|loop]]s being counted twice). We write <math>\de...
3: In a [[directed graph]] the '''indegree''' of a vertex ''v'' is the number of edges terminating at ''v''...
5: ...d a [[regular graph|''k''-regular graph]] and the graph itself is said to have degree ''k''.
7: ...\deg^+(v)=0</math> is called a '''source''' and a vertex with <math>\deg^-(v)=0</math> is called a '''sink...
11: Given a [[directed graph]] ''G'' for each vertex ''v'' of ''G''

Complement (graph theory) (384 bytes)
1: ...h>G</math>. That is, to find the complement of a graph, you fill in all the missing edges, and remove al...
3: [[Category:Graph theory]]

Homeomorphism (graph theory) (967 bytes)
1: ... are usually depicted in illustrations), then two graphs are homeomorphic to each other in the present se...
3: ...ave an edge ''e''={''u'', ''w''}, we insert a new vertex ''v'' and divide ''e'' into two edges {''u'', ''v...
5: For example, if we have the graph ''G''₁
9: ... two graphs are homeomorphic since if we have the graph:
14: [[Category: graph theory]]

Spectral graph theory (1817 bytes)
1: ...r]]s of its [[adjacency matrix]]. An [[undirected graph]] has a [[symmetric matrix|symmetric]] adjacency ...
5: Let ''M'' be the [[adjacency matrix]] of a graph.
7: The [[characteristic polynomial]] of the graph is
9: ...graphs need not be [[isomorphic]], but isomorphic graphs are always isospectral, because the
10: ... polynomial is a [[topological invariant]] of the graph.

Closeness (graph theory) (972 bytes)
1: ...iated with other measures such as [[degree (graph theory)|degree]].
5: ...f geodesic distances to all other vertices in the graph.
13: * [[distance (graph theory)|distance in graphs]]
14: * [[graph theory]].
18: Sabidussi, G. (1966) The centrality index of a graph. ''Pyschometrika'' '''31''', 581--603.

Clique (graph theory) (1010 bytes)
1: [[Category:Graph theory]]
2: ...clique is simply a [[complete graph|complete]] subgraph of G. The size of a clique is the number of verti...
4: ...t algorithm for finding the largest clique of a [[graph]] exists.
6: ... the largest [[independent set]] in the [[inverse graph]].

Tree (graph theory) (3174 bytes)
1: [[Image:Tree_graph.png|right|frame|A tree with 6 vertices and 5 edge...
3: ...cted by ''exactly one'' path. A '''forest''' is a graph in which any two vertices are connected by ''at m...
7: A '''tree''' is an undirected simple graph ''G'' that satisfies any of the following [[equiv...
9: ...raph|connected]] and has no simple [[cycle (graph theory)|cycles]]
10: ...'' has no simple cycles and, if any [[edge (graph theory)|edge]] is added to ''G'', then a simple cycle is...

Extremal graph theory (1774 bytes)
1: '''Extremal graph theory''' is a branch of [[mathematics]].
3: ...h theory''' can encompass a large part of [[graph theory]].
5: ...) as a subgraph? This graph is known as a [[Turán graph]], it contains
7: ... graph not containing ''K''_''k''. This graph has
9: edges. For ''C''_''4'', the largest graph on ''n'' vertices not containing ''C''<sub>''4''<...

Path (graph theory) (1481 bytes)
1: [[Category:Graph theory]]
2: ... an [[edge (graph theory)|edge]] to the successor vertex.
6: ...ths are '''independent''' if they do not have any vertex in common, except the first and last one.
8: ...ing multiple edges multiple times. In the example graph, (1, 2, 5, 1, 2, 3) is a path with length 5, and ...
10: ... graph. The '''weight of a path''' in a weighted graph is the sum of the weights of the traversed edges....

Glossary of graph theory (30722 bytes)
1: One major problem that has plagued [[graph theory]] since its inception is the consistent lack of c...
3: While using this '''glossary of graph theory''', please keep in mind that it is merely a start...
7: A '''graph''' ''G'' consists of two types of elements, namel...
9: ...of a '''directed graph''' or a [[Directed graph|digraph]], see Section [[#Direction|Direction]].
11: Alternative models of ''graph'' exist; e.g., a graph may be thought as a [[Boolean]] [[binary function...

Minor (graph theory) (1392 bytes)
1: ... to a graph that results from a [[graph theory|subgraph]] of ''G'' by zero or more ''edge contractions''....
3: For example, the graph
21: ...a [[partial order]] on the isomorphism classes of graphs.
23: ...'s theorem]] for the characterization of [[planar graph]]s. The general situation is described by the [[R...
25: ...'G''₁, ''G''₂,... of finite graphs is given, then there always exists two indices '...

Rooted product (graph theory) (1080 bytes)
1: ...ake |''V''(''G'')| copies of ''H'', and for every vertex ''v_i'' of ''G'', identify ''v_i'' with the root ...
17: * C. D. Godsil, Brendan D. McKay, ''A new graph product and its spectrum'', Bull. Austral. Math. ...
20: [[Category:Graph theory]]

Connected component (graph theory) (1941 bytes)
1: ... empty space between them. A nonempty [[connected graph]] has one connected component.
3: In an undirected graph, the existence of a path between two vertices ''u...
4: * There is a trivial path of length zero from any vertex to itself. (reflexivity)
9: ...panning forest or maximum matching for the entire graph.
13: * Is a graph connected? Not connected?

List of graph theory topics (4913 bytes)
1: This is a '''list of [[graph theory]] topics''', by Wikipedia page.
3: See [[glossary of graph theory]] for basic terminology
5: ==Examples and types of graphs==
8: *[[Bipartite graph]]
9: **[[Complete bipartite graph]]

Infinite tree (graph theory) (1297 bytes)
1: In [[mathematics]], an '''infinite [[Tree (graph theory)|tree]]''' is a [[partially ordered set]] ([[pose...
5: ...known to be independent of [[Zermelo-Fraenkel set theory]].

Vertex (1024 bytes)
1: In [[geometry]], a '''vertex''' ([[Latin]]: whirl, whirlpool; plural '''vertic...
3: ... (graph theory)|node]] or [[vertex (graph theory)|vertex]]. The connections themselves are called ''edges...
5: In [[3D computer graphics]], a vertex is a point in 3D space with a particular location...

<< Prev 20 Result Pages:   1  2  3  4  5  6  7  8  9  10  Next 20 >>