On the Cayley isomorphism problem

In this paper, we prove several results on the Cayley isomorphism problem concerning undirected graphs. Let φ be Euler's phi function. The main result is the following theorem. Let q1,...,qs be distinct primes and p a prime such that p2 < q1 and p2q1...qi < qi+1 for all 1 ≤ i ≤ s - 1. Let n=q1...qs. If gcd(np,φ(np))= 1, then Zp2 × Zn, is a CI-group with respect to graphs.

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