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Given a point P, the point P^' which is the antipodal point of P is said to be the antipode of P. The term antipode is also used in plane geometry. Given a central conic (or ...

The kth power of a graph G is a graph with the same set of vertices as G and an edge between two vertices iff there is a path of length at most k between them (Skiena 1990, ...

A nonhamiltonian graph is a graph that is not Hamiltonian. All disconnected graphs are therefore nonhamiltoinian, as are acylic graphs. Classes of connected graphs that are ...

The Kuratowski reduction theorem states that very nonplanar graph contains either the utility graph UG=K_(3,3) or the pentatope graph K_5 as a graph minor. The graphs K_(3,3) ...

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 ...

An edge-magic graph is a labeled graph with e graph edges labeled with distinct elements {1,2,...,e} so that the sum of the graph edge labels at each graph vertex is the ...

The Dürer graph is the skeleton of Dürer's solid, which is the generalized Petersen graph GP(6,2). It is illustrated above in a number of embeddings. It is implemented in the ...

A quintic nonhamiltonian graph is a quintic graph that is nonhamiltonian. A number of such graphs are illustrated above. Owens (1980) showed that there exists a ...

The graph difference of graphs G and H is the graph with adjacency matrix given by the difference of adjacency matrices of G and H. A graph difference is defined when the ...

The Moscow-Soicher graph is a weakly regular graph on 672 vertices with parameters (nu,k,lambda,mu)=(672,110,28,(0,18)). It is distance-regular but not distance-transitive ...