Construction of L-equienergetic graphs using some graph operations

For a graph G with n vertices and m edges, the eigenvalues of its adjacency matrix A(G) are known as eigenvalues of G. The sum of absolute values of eigenvalues of G is called the energy of G. The Laplacian matrix of G is defined as where D(G) is the diagonal matrix with entry is the degree of verte...

Full description

Saved in:
Bibliographic Details
Published in:AKCE international journal of graphs and combinatorics 2020-09, Vol.ahead-of-print (ahead-of-print), p.1-6
Main Authors: Vaidya, S. K., Popat, Kalpesh M.
Format: Article
Language:English
Subjects:
Eigenvalue
equienergetic
graph energy
spectrum
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:For a graph G with n vertices and m edges, the eigenvalues of its adjacency matrix A(G) are known as eigenvalues of G. The sum of absolute values of eigenvalues of G is called the energy of G. The Laplacian matrix of G is defined as where D(G) is the diagonal matrix with entry is the degree of vertex v i . The collection of eigenvalues of L(G) with their multiplicities is called spectra of L(G). If are the eigenvalues of L(G) then the Laplacian energy LE(G) of G is defined as It is always interesting and challenging as well to investigate the graphs which are L-equienergetic but L-noncopectral as L-cospectral graphs are obviously L-equienergetic. We have devised a method to construct L-equienergetic graphs which are L-noncospectral.
ISSN:0972-8600
2543-3474
DOI:10.1016/j.akcej.2019.06.012