The cocktail party graph of order n, also called the hyperoctahedral graph, n-octahedron graph O_n, matching graph , or Roberts graph, is the graph consisting of two rows of paired nodes in which all nodes but the paired ones are connected with a graph edge. It is the graph complement (n P_2)^_ of the ladder rung graph n P_2 and the dual graph of the hypercube graph Q_n. It is also the skeleton of the n-cross polytope (which is the origin of its designation as a hyperoctahedral graph by some authors).
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