Ádám's conjecture  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 (), a product of two primes () or satisfies the condition n, φ(n)) = 1, where φ is Euler's function (). 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  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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics