Suppose that and are two Cayley graphs on the cyclic additive group , where is an even integer, , , and are the inverse-closed subsets of . In this paper, it is shown that is a distance-transitive graph, and, by this fact, we determine the adjacency matrix spectrum of . Finally, we show that if and is an even integer, then the adjacency matrix spectrum of is , , , (we write multiplicities as exponents).
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