Abstract
Let k and n be positive integers with n⩾2 k+1, k⩾2. We denote by K= K( n, k) the graph with the k element subsets of {1,…, n} as vertices, where two such vertices are adjacent if they are disjoint. We determine the values of k and n for which K is a Cayley graph. In particular K is not a Cayley graph when n=2 k+1. This answers N.L. Biggs' question as to whether any of the “odd graphs” are Cayley graphs.
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