A graph is said to be integral (resp. distance integral) if all the eigenvalues of its adjacency matrix (resp. distance matrix) are integers. Let H be a finite abelian group, and let
$${\mathscr {H}}=\langle H,b\,|\,b^2=1,bhb=h^{-1},h\in H\rangle $$
be the generalized dihedral group of H. The contribution of this paper is threefold. Firstly, based on the representation theory of finite groups, we obtain a necessary and sufficient condition for a Cayley graph over
$${\mathscr {H}}$$
to be integral, which naturally contains ...
