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A maximal independent edge set of a graph is an independent edge set that cannot be expanded to another independent edge set by addition of any edge in the graph. Note that a ...

The mean distance of a (connected) graph is the mean of the elements of its graph distance matrix. Closed forms for some classes of named graphs are given in the following ...

Given a weighted, undirected graph G=(V,E) and a graphical partition of V into two sets A and B, the cut of G with respect to A and B is defined as cut(A,B)=sum_(i in A,j in ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

A shortest path between two vertices of a graph is a graph path of shortest possible length between them. Such paths are also known as graph geodesics, and the matrix giving ...

The Parts graphs are a set of unit-distance graphs with chromatic number five derived by Jaan Parts in 2019-2020 (Parts 2020a). They provide some of the smallest known ...

The Coxeter configuration is a 12_3 configuration whose Levi graph is the Nauru graph.

The difference between the sum of face angles A_i at a polyhedron vertex of a polyhedron and 2pi, delta=2pi-sum_(i)A_i.

The set closure St^_v of a star Stv at a vertex v of a simplicial complex K.

A set X is called a "cone" with vertex at the origin if for any x in X and any scalar a>=0, ax in X.