Rarity of normal non-CI Cayley digraphs

Characterize the extent to which normal non-CI Cayley digraphs occur, thereby determining whether such digraphs are rare.

Background

The paper discusses the CI-property restricted to normal Cayley digraphs, whose regular right-translation subgroup is normal in the full automorphism group. Li constructed normal non-CI Cayley digraphs over cyclic 2-groups of order at least 8 and conjectured that examples of normal Cayley digraphs failing the CI-property are rare. The present paper establishes several positive results for abelian groups but does not formulate or settle a general classification of such exceptions.