Vipul: Created page with "{{particular undirected graph}} ==Definition== The Coxeter graph is a graph with 28 vertices and 42 edges defined as follows. Start by considering the [[defining ingredient:..."

2012-05-29T21:29:22Z

Created page with "{{particular undirected graph}} ==Definition== The Coxeter graph is a graph with 28 vertices and 42 edges defined as follows. Start by considering the [[defining ingredient:..."

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{{particular undirected graph}}

==Definition==

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

# The vertex set of the Coxeter graph is the set of cycles of length 6 in the Heawood graph.
# 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===

{| class="sortable" border="1"
! Function !! Value !! Explanation
|-
| {{arithmetic function value|size of vertex set|28}} ||
|-
| {{arithmetic function value|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:

{| class="sortable" border="1"
! Function !! Value !! Explanation
|-
| {{arithmetic function value|degree of a vertex|3}} ||
|-
| {{arithmetic function value|eccentricity of a vertex|4}} ||
|}

Coxeter graph - Revision history

Vipul: Created page with "{{particular undirected graph}} ==Definition== The Coxeter graph is a graph with 28 vertices and 42 edges defined as follows. Start by considering the [[defining ingredient:..."