On Laplacian energy of graphs

Kinkar Ch Das; Seyed Ahmad Mojallal

doi:10.1016/j.disc.2014.02.017

On Laplacian energy of graphs

Kinkar Ch Das
, Seyed Ahmad Mojallal

Department of Mathematics

Sungkyunkwan University

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

Abstract

Let G be a graph with n vertices and m edges. Also let ^μ1, ^μ2,.,μn-₁,^μn=0 be the eigenvalues of the Laplacian matrix of graph G. The Laplacian energy of the graph G is defined as LE=LE(G)=Σi=1n|^μi-2mn|. In this paper, we present some lower and upper bounds for LE of graph G in terms of n, the number of edges m and the maximum degree Δ. Also we give a Nordhaus-Gaddum-type result for Laplacian energy of graphs. Moreover, we obtain a relation between Laplacian energy and Laplacian-energy-like invariant of graphs.

Original language	English
Pages (from-to)	52-64
Number of pages	13
Journal	Discrete Mathematics
Volume	325
Issue number	1
DOIs	https://doi.org/10.1016/j.disc.2014.02.017
State	Published - 28 Jun 2014

Keywords

Graph
Laplacian eigenvalues
Laplacian energy
Laplacian matrix
Laplacian-energy-like invariant

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10.1016/j.disc.2014.02.017

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title = "On Laplacian energy of graphs",

abstract = "Let G be a graph with n vertices and m edges. Also let μ1, μ2,.,μn-1,μn=0 be the eigenvalues of the Laplacian matrix of graph G. The Laplacian energy of the graph G is defined as LE=LE(G)=Σi=1n|μi-2mn|. In this paper, we present some lower and upper bounds for LE of graph G in terms of n, the number of edges m and the maximum degree Δ. Also we give a Nordhaus-Gaddum-type result for Laplacian energy of graphs. Moreover, we obtain a relation between Laplacian energy and Laplacian-energy-like invariant of graphs.",

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year = "2014",

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doi = "10.1016/j.disc.2014.02.017",

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T1 - On Laplacian energy of graphs

AU - Das, Kinkar Ch

AU - Mojallal, Seyed Ahmad

PY - 2014/6/28

Y1 - 2014/6/28

N2 - Let G be a graph with n vertices and m edges. Also let μ1, μ2,.,μn-1,μn=0 be the eigenvalues of the Laplacian matrix of graph G. The Laplacian energy of the graph G is defined as LE=LE(G)=Σi=1n|μi-2mn|. In this paper, we present some lower and upper bounds for LE of graph G in terms of n, the number of edges m and the maximum degree Δ. Also we give a Nordhaus-Gaddum-type result for Laplacian energy of graphs. Moreover, we obtain a relation between Laplacian energy and Laplacian-energy-like invariant of graphs.

AB - Let G be a graph with n vertices and m edges. Also let μ1, μ2,.,μn-1,μn=0 be the eigenvalues of the Laplacian matrix of graph G. The Laplacian energy of the graph G is defined as LE=LE(G)=Σi=1n|μi-2mn|. In this paper, we present some lower and upper bounds for LE of graph G in terms of n, the number of edges m and the maximum degree Δ. Also we give a Nordhaus-Gaddum-type result for Laplacian energy of graphs. Moreover, we obtain a relation between Laplacian energy and Laplacian-energy-like invariant of graphs.

KW - Graph

KW - Laplacian eigenvalues

KW - Laplacian energy

KW - Laplacian matrix

KW - Laplacian-energy-like invariant

UR - https://www.scopus.com/pages/publications/84896771892

U2 - 10.1016/j.disc.2014.02.017

DO - 10.1016/j.disc.2014.02.017

M3 - Article

AN - SCOPUS:84896771892

SN - 0012-365X

VL - 325

SP - 52

EP - 64

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1

ER -

On Laplacian energy of graphs

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Keywords

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