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

Constructions of Self-complementary Circulants with No Multiplicative Isomorphisms

“…A classical result of Turner [16] states that any circulant of prime order p is a CI-graph. This has been further extended by Muzychuk [11] who succeeded in showing that any circulant of order p 1 p 2 · · · p k , a product of distinct primes, is necessarily a CI-graph. We shall also need the following result about CI-graphs of odd order proved in [6, Theorem 3.1] that happens to cover the above mentioned result of Turner as well.…”

Non-Cayley-isomorphic self-complementary circulant graphs

“…Recently ( [12], see also [14]), it became known ultimately for which orders there exist non-CI circulant (di)graphs (that is, A Â da Âm's conjecture is false): these are the numbers divisible by 8 or by a square of an odd prime for digraphs and the same numbers with the exception of 8, 9, and 18 for undirected graphs.…”

An Elementary Abelian Group of Rank 4 Is a CI-Group

“…However, the complete classification of CI-groups is still far from being finished, since we do not know which groups of the above type are really CI-groups. Currently all known infinite series of CI-groups belong to the following three classes: the cyclic groups of orders m, 2m, 4m where m is a square-free odd number [22,23]; the elementary abelian groups of rank at most 3 [9,10,12], groups of orders 2p, 3p, p is a prime [4,5].…”