Energy of generalized complements of a graph

Let G be a finite simple graph on n vertices. Let P = {V₁, V₂, V₃, …, V_k} be a partition of vertex set V (G) of order k ≥ 2. For all V_i and V_j in P, i ≠ j, remove the edges between V_i and V_j in graph G and add the edges between V_i and V_j which are not in G. The graph G^Pk thus obtained is called the k−complement of graph G with respect to the partition P. Let P = {V₁, V₂, V₃, …, V_k} be a partition of vertex set V (G) of order k ≥ 1. For each set V_r in P, remove the edges of graph G inside V_r and add the edges of G (the complement of G) joining the vertices of V_r. The graph (formula presented) thus obtained is called the k(i)−complement of graph G with respect to the partition P. Energy of a graph G is the sum of absolute eigenvalues of G. In this paper, we study energy of generalized complements of some families of graph. An effort is made to throw some light on showing variation in energy due to changes in the partition of the graph.