Laplacian energy of generalized complements of a graph

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_k ^P thus obtained is called the k-complement of graph G with respect to a partition P. 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 G_k(i) ^P thus obtained is called the k(i)-complement of graph G with respect to a partition P. In this paper, we study Laplacian energy of generalized complements of some families of graph. An effort is made to throw some light on showing variation in Laplacian energy due to changes in a partition of the graph.