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The edge chromatic number, sometimes also called the chromatic index, of a graph G is fewest number of colors necessary to color each edge of G such that no two edges ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...

The set of all edge automorphisms of G, denoted Aut^*(G). Let L(G) be the line graph of a graph G. Then the edge automorphism group Aut^*(G) is isomorphic to Aut(L(G)), ...

Let S be a collection of subsets of a finite set X. A subset Y of X that meets every member of S is called the vertex cover, or hitting set. A vertex cover of a graph G can ...

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 ...

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 ...