A sharp upper bound on the largest Laplacian eigenvalue of weighted graphs

Kinkar Ch Das; R. B. Bapat

doi:10.1016/j.laa.2005.06.024

A sharp upper bound on the largest Laplacian eigenvalue of weighted graphs

Kinkar Ch Das
, R. B. Bapat

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

32 Scopus citations

Abstract

We consider weighted graphs, where the edge weights are positive definite matrices. The Laplacian of the graph is defined in the usual way. We obtain an upper bound on the largest eigenvalue of the Laplacian and characterize graphs for which the bound is attained. The classical bound of Anderson and Morley, for the largest eigenvalue of the Laplacian of an unweighted graph follows as a special case.

Original language	English
Pages (from-to)	153-165
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	409
Issue number	1-3 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.laa.2005.06.024
State	Published - 1 Nov 2005
Externally published	Yes

Keywords

Laplacian matrix
Largest eigenvalue
Upper bound
Weighted graph

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10.1016/j.laa.2005.06.024

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abstract = "We consider weighted graphs, where the edge weights are positive definite matrices. The Laplacian of the graph is defined in the usual way. We obtain an upper bound on the largest eigenvalue of the Laplacian and characterize graphs for which the bound is attained. The classical bound of Anderson and Morley, for the largest eigenvalue of the Laplacian of an unweighted graph follows as a special case.",

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AU - Bapat, R. B.

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N2 - We consider weighted graphs, where the edge weights are positive definite matrices. The Laplacian of the graph is defined in the usual way. We obtain an upper bound on the largest eigenvalue of the Laplacian and characterize graphs for which the bound is attained. The classical bound of Anderson and Morley, for the largest eigenvalue of the Laplacian of an unweighted graph follows as a special case.

AB - We consider weighted graphs, where the edge weights are positive definite matrices. The Laplacian of the graph is defined in the usual way. We obtain an upper bound on the largest eigenvalue of the Laplacian and characterize graphs for which the bound is attained. The classical bound of Anderson and Morley, for the largest eigenvalue of the Laplacian of an unweighted graph follows as a special case.

KW - Laplacian matrix

KW - Largest eigenvalue

KW - Upper bound

KW - Weighted graph

UR - https://www.scopus.com/pages/publications/24944503889

U2 - 10.1016/j.laa.2005.06.024

DO - 10.1016/j.laa.2005.06.024

M3 - Article

AN - SCOPUS:24944503889

SN - 0024-3795

VL - 409

SP - 153

EP - 165

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3 SPEC. ISS.

ER -

A sharp upper bound on the largest Laplacian eigenvalue of weighted graphs

Abstract

Keywords

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