On Ádámʹs conjecture for circulant graphs

Ádámʹs (1967) conjecture formulates necessary and sufficient conditions for cyclic (circulant) graphs to be isomorphic. It is known that the conjecture fails if n is divisible by either 8 or by an odd square. On the other hand, it was shown in [7] that the conjecture is true for circulant graphs with square-free number of vertices. In this paper we prove that Ádámʹs conjecture remains also true if the number of vertices of a graph is twice squarefree.