Main functions and the spectrum of super graphs

Let A be a graph type and B an equivalence relation on a group G. Let [g] be the equivalence class of g with respect to the equivalence relation B. The B superA graph of G is an undirected graph whose vertex set is G and two distinct vertices g,h∈G are adjacent if [g]=[h] or there exist x∈[g] and y∈[h] such that x and y are adjacent in the A graph of G. In this paper, we compute spectrum of equality/conjugacy supercommuting graphs of dihedral/dicyclic groups and show that these graphs are not integral.