Normal Cayley digraphs of cyclic groups with CI-property

Abstract

A Cayley (di)graph of a group G is called normal if the right regular representation of G is normal in the full automorphism group of and a CI-(di)graph if for every Cayley (di)graph implies that there is such that We call a group G an NDCI-group or NCI-group if all normal Cayley digraphs or graphs of G are CI-digraphs or CI-graphs, respectively. We prove that a cyclic group of order n is an NDCI-group if and only if and an NCI-group if and only if either n = 8 or