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.