Dihedral groups of square-free order are DCI-groups

A finite group G is called a DCI-group if any two isomorphic Cayley digraphs of G are also isomorphic via an automorphism of G . If G is a non-abelian generalised dihedral DCI-group, then Dobson, Muzychuk, and Spiga proved that G must be a dihedral group of square-free order (Ars Math. Contemp., 2022). In this paper, we prove that the converse statement also holds, i.e. all dihedral groups of square-free order are DCI-groups.