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A polyhedron that is dual to itself. For example, the tetrahedron is self-dual. Naturally, the skeleton of a self-dual polyhedron is a self-dual graph. Pyramids are ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

The 10_3 configuration of ten lines intersecting three at a time in 10 points which arises in Desargues' theorem. Its Levi graph is the Desargues graph.

Let v(G) be the number of vertices in a graph G and h(G) the length of the maximum cycle in G. Then the shortness exponent of a class of graphs G is defined by sigma(G)=lim ...

The Bron-Kerbosch algorithm is an efficient method for finding all maximal cliques in a graph.

A node which is one graph edge further away from a given node in a rooted tree.

Iofinova and Ivanov (1985) showed that there exist exactly five bipartite cubic semisymmetric graphs whose automorphism groups preserves the bipartite parts and acts ...

The quadratic embedding constant QEC(G) of a finite simple connected graph G on n vertices is defined as the maximum of the product vDv over all real n-vectors v satisfying ...

A Hamilton decomposition (also called a Hamiltonian decomposition; Bosák 1990, p. 123) of a Hamiltonian regular graph is a partition of its edge set into Hamiltonian cycles. ...

Dijkstra's algorithm is an algorithm for finding a graph geodesic, i.e., the shortest path between two graph vertices in a graph. It functions by constructing a shortest-path ...