Energy of Graph

Authors

  • Najibullah Yousefi Teaching, Assistant Professor, Department of Mathematics, Faculty of Electromechanics, Polytechnic University, AFGHANISTAN.
  • Amrullah Awsar Associate Professor, Department of Mathematics, Faculty of Electromechanics, Polytechnic University, AFGHANISTAN.
  • Laila Popalzai Senior Teaching Assistant Professor, Department of Mathematics, Faculty of Electromechanics, Polytechnic University, AFGHANISTAN.

DOI:

https://doi.org/10.55544/jrasb.2.1.3

Keywords:

Degree matrix, laplacian matrix, Adjacency matrix, spectrum of graph, energy of graph, Laplacian energy of graph

Abstract

By given the adjacency matrix, laplacian matrix of a graph we can find the set of eigenvalues of graph in order to discussed about the energy of graph and laplacian energy of graph. (i.e. the sum of eigenvalues of adjacency matrix and laplacian matrix of a graph is called the energy of graph) and the laplacian energy of graph is greater or equal to zero for any graph and is greater than zero for every connected graph with more or two vertices (i.e. the last eigenvalues of laplacian matrix is zero), according to several theorems about the energy of graph and the laplacian energy of graph that are described in this work; I discussed about energy of graph, laplacian energy of graph and comparing them here.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

References

Department of Mathematics, south china university, Energy and Laplacian Energy of graph, Match commun, Math. compute. chem (2010)

Gutman. B. Zhou, on Laplacian Energy of graph, MATCH Commun Math Comput Chem (2007)

Gutman Ivan Li Xueliang Shi Youngtang Graph Energy Springer New York Heidelberg Dordrecht London (2012)

Mojallal Seyed Ahmad, Energy and laplacian Energy of graph, University of Regina (2016)

R.A. Bruualdi, Laplacian Energy of Graph, Gutman (Ivan.B. Zhou. Linear algebra and its application), (2006)

R. Blalakrishnan, The Energy of graph, Linear Algebra Appl. (2004)

R. Grone, R. Merris, the Laplacian Spectrum of Graph, II SIAM J. Discerete Math (1994)

R. Grone, R. Merris V.S. Sunder, the Laplacian spectrum of a graph. SIAMJ. Matrix Ana Appl (1990)

R. Merris, laplacian matrices of graph, a survey, Linear algebra (1994)

Downloads

Published

2023-02-01

How to Cite

Yousefi, N., Awsar, A., & Popalzai, L. (2023). Energy of Graph. Journal for Research in Applied Sciences and Biotechnology, 2(1), 13–17. https://doi.org/10.55544/jrasb.2.1.3

Issue

Vol. 2 No. 1 (2023): February Issue

Section

Articles

License

Copyright (c) 2023 Najibullah Yousefi, Amrullah Awsar, Laila Popalzai

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC