ON THE GERŠGORIN DISKS OF DISTANCE MATRICES OF GRAPHS

Mustapha Aouchiche; Bilal A. Rather; Issmail El Hallaoui

doi:10.13001/ELA.2021.6489

ON THE GERŠGORIN DISKS OF DISTANCE MATRICES OF GRAPHS

Mustapha Aouchiche
, Bilal A. Rather
, Issmail El Hallaoui

Department of Mathematical Sciences

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

7 Citations (Scopus)

Abstract

For a simple connected graph G, let D(G), T r(G), D^L (G) = T r(G) − D(G), and D^Q (G) = T r(G) + D(G) be the distance matrix, the diagonal matrix of the vertex transmissions, the distance Laplacian matrix, and the distance signless Laplacian matrix of G, respectively. Atik and Panigrahi [2] suggested the study of the problem: Whether all eigenvalues, except the spectral radius, of D(G) and D^Q (G) lie in the smallest Geršgorin disk? In this paper, we provide a negative answer by constructing an infinite family of counterexamples.

Original language	English
Pages (from-to)	709-717
Number of pages	9
Journal	Electronic Journal of Linear Algebra
Volume	37
DOIs	https://doi.org/10.13001/ELA.2021.6489
Publication status	Published - Jan 9 2021

Keywords

Distance Laplacian
Distance matrix
Distance signless Laplacian
Eigenvalues inequalities
Geršgorin disks

ASJC Scopus subject areas

Algebra and Number Theory

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10.13001/ELA.2021.6489

Cite this

@article{85e0f0fb292c453bb5a4c48366c820ce,

title = "ON THE GER{\v S}GORIN DISKS OF DISTANCE MATRICES OF GRAPHS",

abstract = "For a simple connected graph G, let D(G), T r(G), DL (G) = T r(G) − D(G), and DQ (G) = T r(G) + D(G) be the distance matrix, the diagonal matrix of the vertex transmissions, the distance Laplacian matrix, and the distance signless Laplacian matrix of G, respectively. Atik and Panigrahi [2] suggested the study of the problem: Whether all eigenvalues, except the spectral radius, of D(G) and DQ (G) lie in the smallest Ger{\v s}gorin disk? In this paper, we provide a negative answer by constructing an infinite family of counterexamples.",

keywords = "Distance Laplacian, Distance matrix, Distance signless Laplacian, Eigenvalues inequalities, Ger{\v s}gorin disks",

author = "Mustapha Aouchiche and Rather, \{Bilal A.\} and \{El Hallaoui\}, Issmail",

year = "2021",

month = jan,

day = "9",

doi = "10.13001/ELA.2021.6489",

language = "English",

volume = "37",

pages = "709--717",

journal = "Electronic Journal of Linear Algebra",

issn = "1537-9582",

publisher = "International Linear Algebra Society",

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TY - JOUR

T1 - ON THE GERŠGORIN DISKS OF DISTANCE MATRICES OF GRAPHS

AU - Aouchiche, Mustapha

AU - Rather, Bilal A.

AU - El Hallaoui, Issmail

PY - 2021/1/9

Y1 - 2021/1/9

N2 - For a simple connected graph G, let D(G), T r(G), DL (G) = T r(G) − D(G), and DQ (G) = T r(G) + D(G) be the distance matrix, the diagonal matrix of the vertex transmissions, the distance Laplacian matrix, and the distance signless Laplacian matrix of G, respectively. Atik and Panigrahi [2] suggested the study of the problem: Whether all eigenvalues, except the spectral radius, of D(G) and DQ (G) lie in the smallest Geršgorin disk? In this paper, we provide a negative answer by constructing an infinite family of counterexamples.

AB - For a simple connected graph G, let D(G), T r(G), DL (G) = T r(G) − D(G), and DQ (G) = T r(G) + D(G) be the distance matrix, the diagonal matrix of the vertex transmissions, the distance Laplacian matrix, and the distance signless Laplacian matrix of G, respectively. Atik and Panigrahi [2] suggested the study of the problem: Whether all eigenvalues, except the spectral radius, of D(G) and DQ (G) lie in the smallest Geršgorin disk? In this paper, we provide a negative answer by constructing an infinite family of counterexamples.

KW - Distance Laplacian

KW - Distance matrix

KW - Distance signless Laplacian

KW - Eigenvalues inequalities

KW - Geršgorin disks

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U2 - 10.13001/ELA.2021.6489

DO - 10.13001/ELA.2021.6489

M3 - Article

AN - SCOPUS:85123000930

SN - 1537-9582

VL - 37

SP - 709

EP - 717

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

ER -

ON THE GERŠGORIN DISKS OF DISTANCE MATRICES OF GRAPHS

Abstract

Keywords

ASJC Scopus subject areas

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