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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.

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 ...