Laplacian energy of generalized complements of a graph

Abstract

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 = 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 P k 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 P k(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.

Laplacian Energy of a Graph with Self-Loops

“…, λ n (G S ) are the eigenvalues of A(G S ). For more information on energy, Laplacian energy and energy of graph with selfloops, refer [2,5,11,12,15].…”