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The (m,q)-Ustimenko graph is the distance-1 or distance-2 graph of the dual polar graph on [C_m(q)] (Brouwer et al. 1989, p. 279). The Ustimenko graph with parameters m and q ...

A cubic vertex-transitive graph is a cubic graph that is vertex transitive. Read and Wilson (1998, pp. 161-163) enumerate all connected cubic vertex-transitive graphs on 34 ...

The Coxeter graph is a nonhamiltonian cubic symmetric graph on 28 vertices and 42 edges which can be constructed as illustrated above. It can also be constructed as the graph ...

Let P(G) denote the chromatic polynomial of a finite simple graph G. Then G is said to be chromatically unique if P(G)=P(H) implies that G and H are isomorphic graphs, in ...

A graph G is said to be flexible if the vertices of G can be moved continuously so that (1) the distances between adjacent vertices are unchanged, and (2) at least two ...

The (weak) Bruhat graph B_n of order n is the simple graph having have all permutations of {1,2,...,n} as vertices, and with an edge between pairs of permutations that differ ...

The Ljubljana graph is a graph on 112 vertices that is the third smallest cubic semisymmetric graph. It was discovered by Brouwer et al. (1993) and rediscovered by Conder et ...

The Zara graph is the unique graph on 126 vertices satisfying the properties that 1) every maximal clique (of which there are a total of 567) has six vertices, and 2) that if ...

An intrinsically linked graph is a graph having the property that any embedding of it in three dimensions contains a nontrivial link. A graph is intrinsically linked iff it ...

A graph G is a hypotraceable graph if G has no Hamiltonian path (i.e., it is not a traceable graph), but G-v has a Hamiltonian path (i.e., is a traceable graph) for every v ...