The gear graph, also sometimes known as a bipartite wheel graph , is a wheel graph with a graph vertex added between each pair of adjacent graph vertices of the outer cycle. The gear graph G_n has 2n + 1 nodes and 3n edges. The gear graphs G_n are a special case J_(2, n) of the Jahangir graph. Gear graphs are unit-distance and matchstick graphs, as illustrated in the embeddings shown above. Attractive derived unit-distance graph are produced by taking the vertex sets from the matchstick embeddings and connecting all pairs of vertices separate by a unit distance for n = 3, 6, 12, and 18, illustrated above, with the n = 3 case corresponding to the wheel graph W_7.
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