Laplacian Energy of a Fuzzy Graph

Abstract

A concept related to the spectrum of a graph is that of energy. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G . The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues of G and the average degree d(G) of G. In this paper we introduce the concept of Laplacian energy of fuzzy graphs. Let G be a fuzzy graph with n vertices and m edges. The Laplacian spectrum of fuzzy graph G is defined. The Laplacian energy of G has been recently defined . Section 2 consists of preliminaries and definition of Laplacian energy of a fuzzy graph and in Section 3, we present some results on Laplacian energy of a fuzzy graph. Some bounds o Laplacian energy of fuzzy graphs are also given.