Ádám's Conjecture is True in the Square-Free Case

  title={{\'A}d{\'a}m's Conjecture is True in the Square-Free Case},
  author={Mikhail E. Muzychuk},
  journal={J. Comb. Theory, Ser. A},
Ad~im'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, ~b(n))= 1, where ~b 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 Ad/tm's conjecture is true for all other… CONTINUE READING
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