Relation between signless Laplacian energy, energy of graph and its line graph

Kinkar Ch Das; Seyed Ahmad Mojallal

doi:10.1016/j.laa.2015.12.006

Relation between signless Laplacian energy, energy of graph and its line graph

Kinkar Ch Das, Seyed Ahmad Mojallal

Department of Mathematics

Sungkyunkwan University

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

21 Scopus citations

Abstract

The energy of a simple graph G, E(G), is the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of line graph and the signless Laplacian energy of graph G are denoted by E(_LG) (_LG is the line graph of G) and ^LE+(G), respectively. In this paper we obtain a relation between E(_LG) and ^LE+(G) of graph G. From this relation we characterize all the graphs satisfying E(_LG)=^LE+(G)+4mn-4. We also present a relation between E(G) and E(_LG). Moreover, we give an upper bound on E(_LG) of graph G and characterize the extremal graphs.

Original language	English
Pages (from-to)	91-107
Number of pages	17
Journal	Linear Algebra and Its Applications
Volume	493
DOIs	https://doi.org/10.1016/j.laa.2015.12.006
State	Published - 15 Mar 2016

Keywords

Adjacency matrix
Energy
First Zagreb index
Graph
Line graph
Signless Laplacian energy
Signless Laplacian matrix

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10.1016/j.laa.2015.12.006

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title = "Relation between signless Laplacian energy, energy of graph and its line graph",

abstract = "The energy of a simple graph G, E(G), is the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of line graph and the signless Laplacian energy of graph G are denoted by E(LG) (LG is the line graph of G) and LE+(G), respectively. In this paper we obtain a relation between E(LG) and LE+(G) of graph G. From this relation we characterize all the graphs satisfying E(LG)=LE+(G)+4mn-4. We also present a relation between E(G) and E(LG). Moreover, we give an upper bound on E(LG) of graph G and characterize the extremal graphs.",

keywords = "Adjacency matrix, Energy, First Zagreb index, Graph, Line graph, Signless Laplacian energy, Signless Laplacian matrix",

author = "Das, \{Kinkar Ch\} and Mojallal, \{Seyed Ahmad\}",

year = "2016",

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doi = "10.1016/j.laa.2015.12.006",

language = "English",

volume = "493",

pages = "91--107",

journal = "Linear Algebra and Its Applications",

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T1 - Relation between signless Laplacian energy, energy of graph and its line graph

AU - Das, Kinkar Ch

AU - Mojallal, Seyed Ahmad

PY - 2016/3/15

Y1 - 2016/3/15

N2 - The energy of a simple graph G, E(G), is the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of line graph and the signless Laplacian energy of graph G are denoted by E(LG) (LG is the line graph of G) and LE+(G), respectively. In this paper we obtain a relation between E(LG) and LE+(G) of graph G. From this relation we characterize all the graphs satisfying E(LG)=LE+(G)+4mn-4. We also present a relation between E(G) and E(LG). Moreover, we give an upper bound on E(LG) of graph G and characterize the extremal graphs.

AB - The energy of a simple graph G, E(G), is the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of line graph and the signless Laplacian energy of graph G are denoted by E(LG) (LG is the line graph of G) and LE+(G), respectively. In this paper we obtain a relation between E(LG) and LE+(G) of graph G. From this relation we characterize all the graphs satisfying E(LG)=LE+(G)+4mn-4. We also present a relation between E(G) and E(LG). Moreover, we give an upper bound on E(LG) of graph G and characterize the extremal graphs.

KW - Adjacency matrix

KW - Energy

KW - First Zagreb index

KW - Graph

KW - Line graph

KW - Signless Laplacian energy

KW - Signless Laplacian matrix

UR - https://www.scopus.com/pages/publications/84950293316

U2 - 10.1016/j.laa.2015.12.006

DO - 10.1016/j.laa.2015.12.006

M3 - Article

AN - SCOPUS:84950293316

SN - 0024-3795

VL - 493

SP - 91

EP - 107

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Relation between signless Laplacian energy, energy of graph and its line graph

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Keywords

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