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The term energy has an important physical meaning in physics and is an extremely useful concept. There are several forms energy defined in mathematics. In measure theory, let ...

A complete oriented graph (Skiena 1990, p. 175), i.e., a graph in which every pair of nodes is connected by a single uniquely directed edge. The first and second 3-node ...

Wagner's theorem states that a graph is planar iff it does not contain K_5 or K_(3,3) as a graph minor.

Let G be a graph, and suppose each edge of G is independently deleted with fixed probability 0<=p<=1. Then the probability that no connected component of G is disconnected as ...

The Hall-Janko near octagon, also known as the Cohen-Tits near octagon, is a weakly regular graph on 315 vertices with parameters (n,k,lambda,mu)=(315,(10),(1),(0,1)). It is ...

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 Sombor index of a graph is defined as half the sum of the matrix elements of its Sombor matrix.

Let d_G(k) be the number of dominating sets of size k in a graph G, then the domination polynomial D_G(x) of G in the variable x is defined as ...

Let G be a graph with A and B two disjoint n-tuples of graph vertices. Then either G contains n pairwise disjoint AB-paths, each connecting a point of A and a point of B, or ...

The coloring red of two complete subgraphs of n/2 points (for even n) in order to generate a blue-empty graph.