Ádám's conjecture is true in the square-free case

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79 Scopus citations


Ádám's conjecture [1] formulates necessary and sufficient conditions for cyclic (circulant) graphs to be isomorphic. It is known to be true if the number n of vertices is either prime ([4]), a product of two primes ([12]) or satisfies the condition n, φ(n)) = 1, where φ is Euler's function ([15]). On the other hand, it is also known that the conjecture fails if n is divisible by 8 or by an odd square. It was newly conjectured in [15] that Ádám's conjecture is true for all other values of n. We prove that the conjecture is valid whenever n is a square-free number.

Original languageEnglish
Pages (from-to)118-134
Number of pages17
JournalJournal of Combinatorial Theory - Series A
Issue number1
StatePublished - 1 Jan 1995
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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