Perfect state transfer in integral circulant graphs of non-square-free order

This paper provides further results on the perfect state transfer in integral circulant graphs (ICG graphs). The non-existence of PST is proved for several classes of ICG graphs containing an isolated divisor d(0), i.e. the divisor which is relatively prime to all other divisors from d is an element of D\{d(0)}. The same result is obtained for classes of integral circulant graphs having the NSF property (i.e. each n/d is square-free, for every d is an element of D). A direct corollary of these results is the characterization of ICG graphs with two divisors, which have PST. A similar characterization is obtained for ICG graphs where each two divisors are relatively prime. Finally, it is shown that ICG graphs with the number of vertices n = 2p(2) do not have PST. (C) 2010 Elsevier Inc. All rights reserved.