Energy of Partial Complement of a Graph with Self-loops

The purpose of this paper is to extend the concept of energy of a graph with self-loops to partial complement of a graph. The partial complement of a graph G with respect to a set S denoted by G ⊕ S is the graph obtained by removing the edges of ⟨S⟩ and adding edges which are not in ⟨S⟩ in G. Let G be a graph of order n with σ self-loops, then the energy ∑ is defined as (Formula Presented). Based on this, we introduce i=1 n the concept of energy of partial complement of a graph G with self-loops.