Coxeter graph

This article defines a particular undirected graph, i.e., the definition here determines the graph uniquely up to graph isomorphism.
View a complete list of particular undirected graphs

Definition

The Coxeter graph is a graph with 28 vertices and 42 edges defined as follows. Start by considering the Heawood graph:

1. The vertex set of the Coxeter graph is the set of cycles of length 6 in the Heawood graph.
2. The edge set is defined as follows: two vertices of the Coxeter graph are incident if, when viewed as 6-cycles in the Heawood graph, they are vertex-disjoint, i.e., share no common vertices.

Arithmetic functions

Size measures

Function	Value	Explanation
size of vertex set	28
size of edge set	42

Numerical invariants associated with vertices

Since the graph is a vertex-transitive graph, any numerical invariant associated to a vertex must be equal on all vertices of the graph. Below are listed some of these invariants:

Function	Value	Explanation
degree of a vertex	3
eccentricity of a vertex	4