Maximum-size independent sets and automorphism groups of tensor powers of the even derangement graphs

Abstract

Let An be the alternating group of even permutations of X :={1, 2,···, n} andEn the set of even derangements on X. Denote by A q the tensor product of q copies of A n, where the Cayley graph A n := (An,En) is called the even derangement graph. In this paper, we intensively investigate the properties of A q including connectedness, diameter, independence number, clique number, chromatic number and the maximumsize independent sets of A q. By using the result on the maximum-size independent sets A q, we completely determine the full automorphism groups of A q.