Algebraic degrees of 2-Cayley digraphs over abelian groups

A digraph Gamma is called a 2-Cayley digraph over a group G if there exists a 2-orbit semiregular subgroup of Aut(Gamma) isomorphic to G. In this paper, we completely determine the algebraic degrees of 2-Cayley digraphs over abelian groups. This generalizes the main results of Lu and Monius in 2023. As applications, we consider the algebraic degrees of Cayley digraphs over finite groups admitting an abelian subgroup of index 2. Special attention is paid to the algebraic degrees of Cayley (di)graphs over generalized dihedral groups, generalized dicyclic groups and semi-dihedral groups.