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A graph G is the edge graph of a polyhedron iff G is a simple planar graph which is 3-connected.

The triangle graph is the cycle graph C_3, which is isomorphic to the complete graph K_3 as well as to the complete tripartite graph K_(3×1)=K_(1,1,1) and the triangular ...

If a graph G has n graph vertices such that every pair of the n graph vertices which are not joined by a graph edge has a sum of valences which is >=n, then G is Hamiltonian. ...

The Reye graph is the transposition graph G_4 of order 4.

The shortest path-spanning tree from a graph vertex of a graph.

A graph vertex in a graph is said to be an even node if its vertex degree is even.

The cube of a graph is defined as its third graph power.

A reflexive graph is a pseudograph such that each vertex has an associated graph loop.

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.

A graph that is not finite is called infinite.