Bounds on the entries of the principal eigenvector of the distance signless Laplacian matrix

Kinkar Ch Das; Celso M. Da Silva; Maria Aguieiras A. De Freitas; Renata R. Del-Vecchio

doi:10.1016/j.laa.2015.06.003

Bounds on the entries of the principal eigenvector of the distance signless Laplacian matrix

Kinkar Ch Das, Celso M. Da Silva, Maria Aguieiras A. De Freitas, Renata R. Del-Vecchio

Department of Mathematics

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

7 Scopus citations

Abstract

Abstract The distance signless Laplacian spectral radius of a connected graph G is the largest eigenvalue of the distance signless Laplacian matrix of G, defined as D^Q(G)=Tr(G)+D(G), where D(G) is the distance matrix of G and Tr(G) is the diagonal matrix of vertex transmissions of G. In this paper we determine upper and lower bounds on the minimal and maximal entries of the principal eigenvector of D^Q(G) and characterize the extremal graphs. In addition, we obtain a lower bound on the distance signless Laplacian spectral radius of G based on its order and independence number, and characterize the extremal graph.

Original language	English
Article number	13239
Pages (from-to)	200-220
Number of pages	21
Journal	Linear Algebra and Its Applications
Volume	483
DOIs	https://doi.org/10.1016/j.laa.2015.06.003
State	Published - 12 Jun 2015

Keywords

Diameter
Distance signless Laplacian matrix
Independence number
Principal eigenvector
Spectral radius

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title = "Bounds on the entries of the principal eigenvector of the distance signless Laplacian matrix",

abstract = "Abstract The distance signless Laplacian spectral radius of a connected graph G is the largest eigenvalue of the distance signless Laplacian matrix of G, defined as DQ(G)=Tr(G)+D(G), where D(G) is the distance matrix of G and Tr(G) is the diagonal matrix of vertex transmissions of G. In this paper we determine upper and lower bounds on the minimal and maximal entries of the principal eigenvector of DQ(G) and characterize the extremal graphs. In addition, we obtain a lower bound on the distance signless Laplacian spectral radius of G based on its order and independence number, and characterize the extremal graph.",

keywords = "Diameter, Distance signless Laplacian matrix, Independence number, Principal eigenvector, Spectral radius",

author = "Das, \{Kinkar Ch\} and \{Da Silva\}, \{Celso M.\} and \{De Freitas\}, \{Maria Aguieiras A.\} and Del-Vecchio, \{Renata R.\}",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2015",

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doi = "10.1016/j.laa.2015.06.003",

language = "English",

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journal = "Linear Algebra and Its Applications",

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T1 - Bounds on the entries of the principal eigenvector of the distance signless Laplacian matrix

AU - Das, Kinkar Ch

AU - Da Silva, Celso M.

AU - De Freitas, Maria Aguieiras A.

AU - Del-Vecchio, Renata R.

PY - 2015/6/12

Y1 - 2015/6/12

N2 - Abstract The distance signless Laplacian spectral radius of a connected graph G is the largest eigenvalue of the distance signless Laplacian matrix of G, defined as DQ(G)=Tr(G)+D(G), where D(G) is the distance matrix of G and Tr(G) is the diagonal matrix of vertex transmissions of G. In this paper we determine upper and lower bounds on the minimal and maximal entries of the principal eigenvector of DQ(G) and characterize the extremal graphs. In addition, we obtain a lower bound on the distance signless Laplacian spectral radius of G based on its order and independence number, and characterize the extremal graph.

AB - Abstract The distance signless Laplacian spectral radius of a connected graph G is the largest eigenvalue of the distance signless Laplacian matrix of G, defined as DQ(G)=Tr(G)+D(G), where D(G) is the distance matrix of G and Tr(G) is the diagonal matrix of vertex transmissions of G. In this paper we determine upper and lower bounds on the minimal and maximal entries of the principal eigenvector of DQ(G) and characterize the extremal graphs. In addition, we obtain a lower bound on the distance signless Laplacian spectral radius of G based on its order and independence number, and characterize the extremal graph.

KW - Diameter

KW - Distance signless Laplacian matrix

KW - Independence number

KW - Principal eigenvector

KW - Spectral radius

UR - https://www.scopus.com/pages/publications/84930942943

U2 - 10.1016/j.laa.2015.06.003

DO - 10.1016/j.laa.2015.06.003

M3 - Article

AN - SCOPUS:84930942943

SN - 0024-3795

VL - 483

SP - 200

EP - 220

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

M1 - 13239

ER -

Bounds on the entries of the principal eigenvector of the distance signless Laplacian matrix

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Keywords

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