On integral mixed Cayley graphs over non-abelian finite groups admitting an abelian subgroup of index 2

TL;DR

This paper characterizes when mixed Cayley graphs over non-abelian finite groups with an abelian subgroup of index 2 are integral, extending previous results from abelian groups to a broader class.

Contribution

It generalizes and unifies existing characterizations of integral Cayley graphs to include mixed graphs over non-abelian groups with specific subgroup structures.

Findings

Provides a complete characterization of integral mixed Cayley graphs in the specified class.

Extends known results from abelian to certain non-abelian groups.

Unifies previous characterizations under a broader framework.

Abstract

Recently, several works by a number of authors have provided characterizations of integral undirected Cayley graphs over generalized dihedral groups and generalized dicyclic groups. We generalize and unify these results in two different ways. Firstly, we work over arbitrary non-abelian finite groups admitting an abelian subgroup of index 2. Secondly, our main result actually characterizes integral mixed Cayley graphs over such finite groups, in the spirit of a very recent result of Kadyan--Bhattarcharjya in the abelian case.