Wheel graph

Wheel graph
Wheel graph
	Several examples of wheel graphs
Vertices	n ≥ 4
Edges	2(n − 1)
Diameter	2 if n > 4; 1 if n = 4
Girth	3
Chromatic number	4 if n is even; 3 if n is odd
Spectrum	;
Properties	Hamiltonian; Self-dual; Planar
Notation	Wn
	Table of graphs and parameters

In graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with $n$ vertices can also be defined as the 1-skeleton of an ( $n - 1$ )-gonal pyramid.

Some authors write $W n$ to denote a wheel graph with $n$ vertices ( $n \geq 4$ ); other authors instead use $W n$ to denote a wheel graph with $n + 1$ vertices ( $n \geq 3$ ), which is formed by connecting a single vertex to all vertices of a cycle of length $n$ . The former notation is used in the rest of this article and in the table on the right.

Wheel graph
Several examples of wheel graphs
Vertices	$n \geq 4$
Edges	$2(n - 1)$
Diameter	2 if $n > 4$ 1 if $n = 4$
Girth	3
Chromatic number	4 if $n$ is even 3 if $n$ is odd
Spectrum	$\{2\cos(2k\pi /(n-1))^{1};$ $k=1,\ldots ,n-2\}$ $\cup \{1\pm {\sqrt {n}}\}$
Properties	Hamiltonian Self-dual Planar
Notation	$W n$
Table of graphs and parameters