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The Pasch graph is the Levi graph of the Pasch configuration. The Pasch graph is edge-transitive but not vertex-transitive, but fails to be semisymmetric since it is not ...

The Higman-Sims graph is the unique strongly regular graph on 100 nodes (Higman and Sims 1968, Brouwer 1983, Brouwer and Haemers 1993). It was also constructed independently ...

Tutte's (46-vertex) graph is a cubic nonhamiltonian graph contructed by Tutte (1946) as a counterexample to Tait's Hamiltonian graph conjecture by using three copies ...

The Harries-Wong 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 graph. The Harries-Wong graph ...

There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...

A Moore graph of type (v,g) is a regular graph of vertex degree v>2 and girth g that contains the maximum possible number of nodes, namely ...

A 1-factor of a graph G with n graph vertices is a set of n/2 separate graph edges which collectively contain all n of the graph vertices of G among their endpoints.

Let G be a group, and let S subset= G be a set of group elements such that the identity element I not in S. The Cayley graph associated with (G,S) is then defined as the ...

A quartic vertex-transitive graph is a quartic graph that is vertex transitive. Read and Wilson (1988, pp. 164-166) enumerate all connected quartic vertex-transitive graphs ...