COMPUTING THE EIGENVALUES OF CAYLEY GRAPHS OF ORDER p²q

A graph is called symmetric if its full automorphism group acts transitively on the set of arcs. The Cayley graph Γ = Cay(G, S) on group G is said to be normal symmetric if NA(R(G)) = R(G) ⋊ Aut(G, S) and NA(R(G)) acts transitively on the set of arcs of Γ. In this paper, we determine the spectra of all connected minimal normal symmetric Cayley graphs of order p²q, where p, q are prime numbers.