Energy of Generalized Complements of a Graph

Let G be a finite simple graph on n vertices. Let P = {V-1, V-2, V-3, ..., V-k} be a partition of vertex set V (G) of order k >= 2. For all V-i and V-j in P, i not equal 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(k)(P) thus obtained is called the k- complement of graph G with respect to the partition P. Let P = {V-1, V-2, V-3, ..., 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) over bar (the complement of G) joining the vertices of V-r. The graph G(k(i))(P) 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.