A sharp upper bound on the spectral radius of weighted graphs

Kinkar Ch Das; R. B. Bapat

doi:10.1016/j.disc.2007.06.020

A sharp upper bound on the spectral radius of weighted graphs

Kinkar Ch Das, R. B. Bapat

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

34 Scopus citations

Abstract

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain an upper bound on the spectral radius of the adjacency matrix and characterize graphs for which the bound is attained.

Original language	English
Pages (from-to)	3180-3186
Number of pages	7
Journal	Discrete Mathematics
Volume	308
Issue number	15
DOIs	https://doi.org/10.1016/j.disc.2007.06.020
State	Published - 6 Aug 2008
Externally published	Yes

Keywords

Adjacency matrix
Spectral radius
Upper bound
Weighted graph

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10.1016/j.disc.2007.06.020

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title = "A sharp upper bound on the spectral radius of weighted graphs",

abstract = "We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain an upper bound on the spectral radius of the adjacency matrix and characterize graphs for which the bound is attained.",

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

author = "Das, \{Kinkar Ch\} and Bapat, \{R. B.\}",

year = "2008",

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doi = "10.1016/j.disc.2007.06.020",

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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 eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain an upper bound on the spectral radius of the adjacency matrix and characterize graphs for which the bound is attained.

AB - We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain an upper bound on the spectral radius of the adjacency matrix and characterize graphs for which the bound is attained.

KW - Adjacency matrix

KW - Spectral radius

KW - Upper bound

KW - Weighted graph

UR - https://www.scopus.com/pages/publications/43249087521

U2 - 10.1016/j.disc.2007.06.020

DO - 10.1016/j.disc.2007.06.020

M3 - Article

AN - SCOPUS:43249087521

SN - 0012-365X

VL - 308

SP - 3180

EP - 3186

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 15

ER -

A sharp upper bound on the spectral radius of weighted graphs

Abstract

Keywords

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