Xue Yi HUANG, Qiong Xiang HUANG, Lu LU
Let p be an odd prime, and D2p =<a, b|ap = b2 = 1, bab = a-1 the dihedral group of order 2p. In this paper, we completely classify the cubic Cayley graphs on D2p up to isomorphism by means of spectral method. By the way, we show that two cubic Cayley graphs on D2p are isomorphic if and only if they are cospectral. Moreover, we obtain the number of isomorphic classes of cubic Cayley graphs on D2p by using Gauss' celebrated law of quadratic reciprocity.