Let (G, ∗) be a finite group and S = {x ∈ G|x = x−1} be a subset of G containing its
non-self invertible elements. The inverse graph of G denoted by (G) is a graph whose
set of vertices coincides with G such that two distinct vertices x and y are adjacent if
either x ∗ y ∈ S or y ∗ x ∈ S. In this paper, we study the energy of the dihedral and
symmetric groups, we show that if G is a finite non-abelian group with exactly two
non-self invertible elements, then the associated inverse graph (G) is never a
complete bipartite graph. Furthermore, we establish the isomorphism between the
inverse graphs of a subgroup Dp of the dihedral group Dn of order 2p and subgroup Sk
of the symmetric groups Sn of order k! such that 2p = n! (p, n, k ≥ 3 and p, n, k ∈ Z+).