A Classification of Spectrum-determined Circulant Digraphs

Some researchers have proved that adam’s conjecture is wrong. However, under special conditions, it is right. Let Zn be a cyclic group of order n and Cn(S) be the circulant digraph of Zn with respect to S ⊆ Zn\{0}. In the literature, some people have used a spectral method to solve the isomorphism for the circulants of prime-power order. In this paper, we also use the spectral method to characterize the circulants of order paqbwc(where p, q and w are all distinct primes), and to make adam’s conjecture right.