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2. Cut (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Cut_(graph_theory)

   A cut C = (S, T) is a partition of V of a graph G = (V, E) into two subsets S and T. The cut-set of a cut C = (S, T) is the set {(u, v) ∈ E | u ∈ S, v ∈ T} of edges that have one endpoint in S and the other endpoint in T. If s and t are specified vertices of the graph G, then an s – t cut is a cut in which s belongs to the set S and t ...

3. Vertex separator - Wikipedia

   en.wikipedia.org/wiki/Vertex_separator

   Let S be an (a,b)-separator, that is, a vertex subset that separates two nonadjacent vertices a and b. Then S is a minimal (a,b)-separator if no proper subset of S separates a and b. More generally, S is called a minimal separator if it is a minimal separator for some pair (a,b) of nonadjacent vertices.

4. Glossary of graph theory - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_graph_theory

   A vertex (plural vertices) is (together with edges) one of the two basic units out of which graphs are constructed. Vertices of graphs are often considered to be atomic objects, with no internal structure. vertex cut separating set A set of vertices whose removal disconnects the graph. A one-vertex cut is called an articulation point or cut vertex.

5. Biconnected component - Wikipedia

   en.wikipedia.org/wiki/Biconnected_component

   Multi-colored vertices are cut vertices, and thus belong to multiple biconnected components. In graph theory, a biconnected component or block (sometimes known as a 2-connected component) is a maximal biconnected subgraph. Any connected graph decomposes into a tree of biconnected components called the block-cut tree of the graph.

6. Shannon switching game - Wikipedia

   en.wikipedia.org/wiki/Shannon_switching_game

   Generalized Hex is played on a graph, just like the Shannon game, but instead of coloring the edges, in Hex the players color the vertices. These games have completely different structure and properties. Another connectivity game played with paper and pencil on a rectangular array of dots (or graph paper) is the children's game of "dots and ...

7. Vertex (geometry) - Wikipedia

   en.wikipedia.org/wiki/Vertex_(geometry)

   where V is the number of vertices, E is the number of edges, and F is the number of faces. This equation is known as Euler's polyhedron formula. Thus the number of vertices is 2 more than the excess of the number of edges over the number of faces. For example, since a cube has 12 edges and 6 faces, the formula implies that it has eight vertices.

8. Menger's theorem - Wikipedia

   en.wikipedia.org/wiki/Menger's_theorem

   The vertex-connectivity statement of Menger's theorem is as follows: . Let G be a finite undirected graph and x and y two nonadjacent vertices. Then the size of the minimum vertex cut for x and y (the minimum number of vertices, distinct from x and y, whose removal disconnects x and y) is equal to the maximum number of pairwise internally disjoint paths from x to y.

9. Complete graph - Wikipedia

   en.wikipedia.org/wiki/Complete_graph

   They are maximally connected as the only vertex cut which disconnects the graph is the complete set of vertices. The complement graph of a complete graph is an empty graph. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament. K n can be decomposed into n trees T i such that T i has ...