Abstract
Let An be the alternating group of degree n. Set S={(123),(132),(12)(3i):4≤i≤n}. The alternating group network, denoted by ANn, is defined as the Cayley graph on An with respect to S. The fixing number of a graph Γ is the minimum size of a subset T⊆V(Γ) such that only the identity automorphism of Γ fixes every vertex in T. In this paper, we completely determine the full automorphism group of ANn. Based on this result, we further show that the fixing number of ANn is 2. In addition, we also obtain the independence number and the domination number of ANn.
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