On Ádám's conjecture for circulant graphs

doi:10.1016/S0012-365X(96)00251-8

Discrete Mathematics

Volumes 167–168, 15 April 1997, Pages 497-510

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Abstract

Ádám's (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 [?] that the conjecture is true for circulant graphs with square-free number of vertices. In this paper we prove that Ádám's conjecture remains also true if the number of vertices of a graph is twice square-free.

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¹: Partially supported by the Ministry of Science of Israel and by German-Israeli Foundation for Scientific Research and Development.