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.
Wang et al. (Fri,) studied this question.