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Recently, several works by a number of authors have providedcharacterizations of integral undirected Cayley graphs over generalizeddihedral groups and generalized dicyclic groups. We generalize and unify theseresults in two different ways. Firstly, we work over arbitrary non-abelianfinite groups admitting an abelian subgroup of index 2. Secondly, our mainresult actually characterizes integral mixed Cayley graphs over such finitegroups, in the spirit of a very recent result of Kadyan--Bhattarcharjya in theabelian case.

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