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A minimum vertex cut of a graph is a vertex cut of smallest possible size. A vertex cut set of size 1 in a connected graph corresponds to an articulation vertex. The size of ...

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

An algorithm which can be used to find a good, but not necessarily minimal, edge or vertex coloring for a graph. However, the algorithm does minimally color complete ...

The Descartes snarks are a set of snarks on 210 vertices and 315 edges discovered by William Tutte in 1948 writing under the pseudonym Blanche Descartes (Descartes 1948; ...

The mathematical study of the properties of the formal mathematical structures called graphs.

A generalized octagon GO(n,k) is a generalized polygon of order 8. GO(1,2) is the (3,8)-cage graph, the incidence graph of the Cremona-Richmond configuration, the cubic ...

A pair of vertices (x,y) of a graph G is called an omega-critical pair if omega(G+xy)>omega(G), where G+xy denotes the graph obtained by adding the edge xy to G and omega(H) ...

A connected dominating set in a connected graph G is a dominating set in G whose vertices induce a connected subgraph, i.e., one in which there is no dominating vertex not ...

The adjacency matrix, sometimes also called the connection matrix, of a simple labeled graph is a matrix with rows and columns labeled by graph vertices, with a 1 or 0 in ...

The Balaban 10-cage is one of the three (3,10)-cage graphs (Read and Wilson 1998, p. 272). The Balaban (3,10)-cage was the first known example of a 10-cage (Balaban 1973, ...