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

Department of Mathematics

GERAD and HEC Montreal

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

13 Scopus citations

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
State	Published - 2 Nov 2019

Keywords

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

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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, diameter, Distance Laplacian eigenvalues, distance signless Laplacian eigenvalues, domination number, independence number",

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

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doi = "10.1080/03081087.2018.1491522",

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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

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 - diameter

KW - Distance Laplacian eigenvalues

KW - distance signless Laplacian eigenvalues

KW - domination number

KW - independence number

UR - https://www.scopus.com/pages/publications/85049634232

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

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