On distance Laplacian and distance signless Laplacian eigenvalues of graphs

Kinkar Ch Das; Mustapha Aouchiche; Pierre Hansen

doi:10.1080/03081087.2018.1491522

On distance Laplacian and distance signless Laplacian eigenvalues of graphs

Kinkar Ch Das, Mustapha Aouchiche, Pierre Hansen

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

8 Citations (Scopus)

Abstract

Let D(G),D^L(G) = Diag(Tr) − D(G) and D^Q(G) = Diag(Tr) + D(G) be, respectively, the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix of graph G, where Diag(Tr) denotes the diagonal matrix of the vertex transmissions in G. The eigenvalues of of D^L(G) andD^Q(G) will be denoted by (Formula presented.) and (Formula presented.), respectively. In this paper, we study the properties of the distance Laplacian eigenvalues and the distance signless Laplacian eigenvalues of graph G.

Original language	English
Pages (from-to)	2307-2324
Number of pages	18
Journal	Linear and Multilinear Algebra
Volume	67
Issue number	11
DOIs	https://doi.org/10.1080/03081087.2018.1491522
Publication status	Published - Nov 2 2019
Externally published	Yes

Keywords

05C05
Distance Laplacian eigenvalues
diameter
distance signless Laplacian eigenvalues
domination number
independence number

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/03081087.2018.1491522

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title = "On distance Laplacian and distance signless Laplacian eigenvalues of graphs",

abstract = "Let D(G),DL(G) = Diag(Tr) − D(G) and DQ(G) = Diag(Tr) + D(G) be, respectively, the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix of graph G, where Diag(Tr) denotes the diagonal matrix of the vertex transmissions in G. The eigenvalues of of DL(G) andDQ(G) will be denoted by (Formula presented.) and (Formula presented.), respectively. In this paper, we study the properties of the distance Laplacian eigenvalues and the distance signless Laplacian eigenvalues of graph G.",

keywords = "05C05, Distance Laplacian eigenvalues, diameter, distance signless Laplacian eigenvalues, domination number, independence number",

author = "Das, {Kinkar Ch} and Mustapha Aouchiche and Pierre Hansen",

note = "Funding Information: The first author was supported by the Sungkyun Research Fund, Sungkyunkwan University, 2017, and National Research Foundation of the Korean government with grant No. 2017R1D1A1B03028642. The authors are grateful to the anonymous referee for helpful suggestions and valuable comments, which led to an improvement of the original manuscript. Publisher Copyright: {\textcopyright} 2018, {\textcopyright} 2018 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2019",

month = nov,

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doi = "10.1080/03081087.2018.1491522",

language = "English",

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journal = "Linear and Multilinear Algebra",

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publisher = "Taylor and Francis Ltd.",

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TY - JOUR

T1 - On distance Laplacian and distance signless Laplacian eigenvalues of graphs

AU - Das, Kinkar Ch

AU - Aouchiche, Mustapha

AU - Hansen, Pierre

N1 - Funding Information: The first author was supported by the Sungkyun Research Fund, Sungkyunkwan University, 2017, and National Research Foundation of the Korean government with grant No. 2017R1D1A1B03028642. The authors are grateful to the anonymous referee for helpful suggestions and valuable comments, which led to an improvement of the original manuscript. Publisher Copyright: © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2019/11/2

Y1 - 2019/11/2

N2 - Let D(G),DL(G) = Diag(Tr) − D(G) and DQ(G) = Diag(Tr) + D(G) be, respectively, the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix of graph G, where Diag(Tr) denotes the diagonal matrix of the vertex transmissions in G. The eigenvalues of of DL(G) andDQ(G) will be denoted by (Formula presented.) and (Formula presented.), respectively. In this paper, we study the properties of the distance Laplacian eigenvalues and the distance signless Laplacian eigenvalues of graph G.

AB - Let D(G),DL(G) = Diag(Tr) − D(G) and DQ(G) = Diag(Tr) + D(G) be, respectively, the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix of graph G, where Diag(Tr) denotes the diagonal matrix of the vertex transmissions in G. The eigenvalues of of DL(G) andDQ(G) will be denoted by (Formula presented.) and (Formula presented.), respectively. In this paper, we study the properties of the distance Laplacian eigenvalues and the distance signless Laplacian eigenvalues of graph G.

KW - 05C05

KW - Distance Laplacian eigenvalues

KW - diameter

KW - distance signless Laplacian eigenvalues

KW - domination number

KW - independence number

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UR - http://www.scopus.com/inward/citedby.url?scp=85049634232&partnerID=8YFLogxK

U2 - 10.1080/03081087.2018.1491522

DO - 10.1080/03081087.2018.1491522

M3 - Article

AN - SCOPUS:85049634232

SN - 0308-1087

VL - 67

SP - 2307

EP - 2324

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 11

ER -

On distance Laplacian and distance signless Laplacian eigenvalues of graphs

Abstract

Keywords

ASJC Scopus subject areas

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