Extremal graph characterization from the upper bound of the Laplacian spectral radius of weighted graphs

Kinkar Ch Das

doi:10.1016/j.laa.2007.06.018

Extremal graph characterization from the upper bound of the Laplacian spectral radius of weighted graphs

Kinkar Ch Das

Université Paris-Saclay

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

9 Scopus citations

Abstract

We consider weighted graphs, where the edge weights are positive definite matrices. In this paper, we obtain two upper bounds on the spectral radius of the Laplacian matrix of weighted graphs and characterize graphs for which the bounds are attained. Moreover, we show that some known upper bounds on the Laplacian spectral radius of weighted and unweighted graphs can be deduced from our upper bounds.

Original language	English
Pages (from-to)	55-69
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	427
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2007.06.018
State	Published - 1 Nov 2007
Externally published	Yes

Keywords

Laplacian matrix
Spectral radius
Upper bound
Weighted graph

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10.1016/j.laa.2007.06.018

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title = "Extremal graph characterization from the upper bound of the Laplacian spectral radius of weighted graphs",

abstract = "We consider weighted graphs, where the edge weights are positive definite matrices. In this paper, we obtain two upper bounds on the spectral radius of the Laplacian matrix of weighted graphs and characterize graphs for which the bounds are attained. Moreover, we show that some known upper bounds on the Laplacian spectral radius of weighted and unweighted graphs can be deduced from our upper bounds.",

keywords = "Laplacian matrix, Spectral radius, Upper bound, Weighted graph",

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AU - Das, Kinkar Ch

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N2 - We consider weighted graphs, where the edge weights are positive definite matrices. In this paper, we obtain two upper bounds on the spectral radius of the Laplacian matrix of weighted graphs and characterize graphs for which the bounds are attained. Moreover, we show that some known upper bounds on the Laplacian spectral radius of weighted and unweighted graphs can be deduced from our upper bounds.

AB - We consider weighted graphs, where the edge weights are positive definite matrices. In this paper, we obtain two upper bounds on the spectral radius of the Laplacian matrix of weighted graphs and characterize graphs for which the bounds are attained. Moreover, we show that some known upper bounds on the Laplacian spectral radius of weighted and unweighted graphs can be deduced from our upper bounds.

KW - Laplacian matrix

KW - Spectral radius

KW - Upper bound

KW - Weighted graph

UR - https://www.scopus.com/pages/publications/79953213051

U2 - 10.1016/j.laa.2007.06.018

DO - 10.1016/j.laa.2007.06.018

M3 - Article

AN - SCOPUS:79953213051

SN - 0024-3795

VL - 427

SP - 55

EP - 69

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

ER -

Extremal graph characterization from the upper bound of the Laplacian spectral radius of weighted graphs

Abstract

Keywords

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