Laplacian energy of partial complement of a graph

Abstract

The energy of the graph had its genesis in 1978. It is the sum of absolute values of its eigenvalues. It originates from the π -electron energy in the Huckel molecular orbital model but has also gained purely mathematical interest. Suppose μ1,μ2,…,μn is the Laplacian eigenvalues of G. The Laplacian energy of G has recently been defined as LE(G)=∑i=1nμi-2mn. In this paper, we define Laplacian energy of partial complements of a graph. Laplacian energy and spectrum of partial complements of the few classes of graphs are established. Some bounds and properties of Laplacian energy are obtained.