Abstract
We study covering graphs of the Paley graph associated to a finite field of characteristic p in the case where the covering transformation group is cyclic of prime order distinct from p. When the field has q = p elements, we show that the eigenvalues of the adjacency matrix determine the graph isomorphism class among translation invariant covers. When q = p^r > p, we construct examples of cospectral covering graphs that are not isomorphic as graphs.
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