Perfect state transfer in integral circulant graphs of non square-free order
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چکیده
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 d0, i.e. the divisor which is relatively prime to all other divisors from d ∈ D \ {d0}. The same result is obtained for classes of integral circulant graphs having the NSF property (i.e. each n/d is squarefree, for every d ∈ 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 do not have PST. AMS Subj. Class.: 05C12, 05C50
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تاریخ انتشار 2010