Wheel graph

In the mathematical discipline of 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 ≥ 4); other authors instead use W_n to denote a wheel graph with n + 1 vertices (n ≥ 3), which is formed by connecting a single vertex to all vertices of a cycle of length n. The rest of this article uses the former notation.

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	${\displaystyle \{2\cos(2k\pi /(n-1))^{1};}$ ${\displaystyle k=1,\ldots ,n-2\}}$${\displaystyle \cup \{1\pm {\sqrt {n}}\}}$
Properties	Hamiltonian Self-dual Planar
Notation	Wn
Table of graphs and parameters