A wheel graph of order , sometimes simply called an -wheel (Harary 1994, p. 46; Pemmaraju and Skiena 2003, p. 248; Tutte 2005, p. 78), is a graph that contains a cycle of order , and for which every graph vertex in the cycle is connected to one other graph vertex (which is known as the hub). The edges of a wheel which include the hub are called spokes (Skiena 1990, p. 146). The wheel can be defined as the graph , where is the singleton graph and is the cycle graph. Note that there are two conventions for the indexing for wheel graphs, with some authors (e.g., Gallian 2007), adopting the convention that denotes the wheel graph on nodes.The tetrahedral graph (i.e., ) is isomorphic to , and is isomorphic to the complete tripartite graph . In general, the -wheel graph is the skeleton of an -pyramid. is one of the two graphs obtained by removing two edges from the pentatope graph , the other being the house X graph.Wheel graphs are graceful (Frucht..