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The toroidal crossing number cr_(1)(G) of a graph G is the minimum number of crossings with which G can be drawn on a torus. A planar graph has toroidal crossing number 0, ...

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 ...

The cubic Archimedean graph on 60 nodes and 90 edges that is the skeleton of the truncated dodecahedron. It is implemented in the Wolfram Language as ...

A graph G is k-factorable if it is the union of disjoint k-factors (Skiena 1990, p. 244).

An Ore graph is a graph that satisfies Ore's theorem, i.e., a graph G for which the sums of the degrees of nonadjacent vertices is greater than or equal to the number of ...

Given a planar graph G, a geometric dual graph and combinatorial dual graph can be defined. Whitney showed that these are equivalent (Harary 1994), so that one may speak of ...

Let G be a finite, connected, undirected graph with graph diameter d(G) and graph distance d(u,v) between vertices u and v. A radio labeling of a graph G is labeling using ...

The assignment of labels or colors to the edges or vertices of a graph. The most common types of graph colorings are edge coloring and vertex coloring.

The Sombor energy of a graph is defined as the graph energy of its Sombor matrix, i.e., the sum of the absolute values of the eigenvalues of its Sombor matrix.

The center of a graph G is the set of vertices of graph eccentricity equal to the graph radius (i.e., the set of central points). In the above illustration, center nodes are ...