Recent Advancements in Graph Theory

31L-Spectra of Graphs Obtained by Duplicating Graphs Elements

S. K. Vaidya

Saurashtra University,Rajkot, Gujarat (INDIA)Email: [e-mail]

K. M. Popat

Atmiya University,Rajkot, Gujarat (INDIA)Email: [e-mail]

The concept of L-energy is a concept that stems from energy of graphs. The energy of a graph G is defined with the help of adjacency matrix A(G). The Laplacian matrix of G is defined as L(G) = D(G) − A(G), where D(G) is the diagonal matrix with (ii)^th entry as a degree of vertex v_i. The collection of eigenvalues of L(G) together with their multiplicities is known as L-spectra of G. We have investigated L-spectra for the graphs obtained by means of duplication of graph elements.

31.1Introduction

We begin with ...