Let be a graph. If all the eigenvalues of the adjacency matrix of the graph are integers, then we say that is an integral graph. A graph is determined by its spectrum if every graph cospectral to it is in fact isomorphic to it. In this paper, we investigate some algebraic properties of the Cayley graph , where ( is a prime integer and ) and . First, we show that is an integral graph. Also, we determine the automorphism group of . Moreover, we show that and are determined by their spectrum.
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