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A polyhedral graph is completely regular if the dual graph is also regular. There are only five types. Let rho be the number of graph edges at each node, rho^* the number of ...

A graph Gamma is locally Petersen if, for each point t of Gamma, the graph induced by Gamma on all points adjacent to t (i.e., the neighborhood graph) is isomorphic to the ...

An automorphic graph is a distance-transitive graph Gamma for which the automorphism group Aut(Gamma) acts primitively on the vertices of Gamma and is not a complete graph or ...

The dimension e(G), also called the Euclidean dimension (e.g., Buckley and Harary 1988) of a graph, is the smallest dimension n of Euclidean n-space in which G can be ...

A planar graph G is said to be triangulated (also called maximal planar) if the addition of any edge to G results in a nonplanar graph. If the special cases of the triangle ...

A quintic symmetric graph is a quintic graph (i.e., regular of degree 5) that is also symmetric. Since quintic graphs exist only on an even number of nodes, so do symmetric ...

The cocktail party graph of order n, also called the hyperoctahedral graph (Biggs 1993, p. 17), n-octahedron graph O_n (Jungerman and Ringel 1978), matching graph (Arvind et ...

A regular graph that is edge-transitive but not vertex-transitive is called a semisymmetric graph (Marušič and Potočnik 2001). In contrast, any graph that is both ...

The Harries graph is one of the three (3,10)-cage graphs, the other two being the (10,3)-cage known as the Balaban 10-cage and the Harries-Wong graph. The Harries graph is ...

An identity graph, sometimes also known as an asymmetric graph or rigid graph (Albertson and Collins 1996), is a graph possessing a single graph automorphism. The numbers of ...