Integral Cayley graphs over a certain nonabelian group

A graph [Formula: see text] is said to be integral if all its adjacency eigenvalues are integers. For odd [Formula: see text], Cheng, Feng and Liu gave some necessary or sufficient conditions for the integrality of Cayley graph on nonabelian group [Formula: see text] in the paper “Integral Cayley graphs over a certain nonabelian group, Linear and Multilinear Algebra, 70(21): 7224-7235, 2022”. Meanwhile, it is pointed out that the problem in the aforementioned study may be considered for even [Formula: see text]. Therefore, to provide readers with a complete characterization on the integrality of Cayley graphs over [Formula: see text], we present some necessary or sufficient conditions for the case when [Formula: see text] is even.