  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 $g, h \in G$ are adjacent if $[g] = [h]$ or there exist $x
\in [g]$ and $y \in [h]$ 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.
