Laplacian energy of generalized complements of a graph

Abstract

Let P = {V1, V2, V3, . . . , Vk} be a partition of vertex set V (G) of order k ≥ 2. For all Vi and Vj in P, ≠ 6= j, remove the edges between Vi and Vj in graph G and add the edges between Vi and Vj which are not in G. The graph GPk thus obtained is called the k-complement of graph G with respect to a partition P. For each set Vr in P, remove the edges of graph G inside Vr and add the edges of G (the complement of G) joining the vertices of Vr. The graph GPk (i) 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.