High Quality Content by WIKIPEDIA articles! In the mathematical discipline of graph theory, a wheel graph Wn is a graph with n vertices, formed by connecting a single vertex to all vertices of an (n-1)-cycle. The numerical notation for wheels is used inconsistently in the literature: some authors instead use n to refer to the length of the cycle, so that their Wn is the graph we denote Wn+1. A wheel graph can also be defined as the 1-skeleton of an (n-1)-gonal pyramid. Wheel graphs are planar graphs, and as such have a unique planar embedding. More specifically, every wheel graph is a Halin graph. They are self-dual: the planar dual of any wheel graph is an isomorphic graph. Any maximal planar graph, other than K4 = W4, contains as a subgraph either W5 or W6.

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