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Wheel graph
Cycle graph plus universal vertex / From Wikipedia, the free encyclopedia
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[1] write Wn to denote a wheel graph with n vertices (n ≥ 4); other authors[2] instead use Wn 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.
Quick Facts Vertices, Edges ...
Wheel graph | |
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![]() 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 |
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