Extremal graph characterization from the bounds of the spectral radius of weighted graphs

Kinkar Ch Das

doi:10.1016/j.amc.2011.02.033

Extremal graph characterization from the bounds of the spectral radius of weighted graphs

Kinkar Ch Das

Department of Mathematics

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

12 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 a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained.

Original language	English
Pages (from-to)	7420-7426
Number of pages	7
Journal	Applied Mathematics and Computation
Volume	217
Issue number	18
DOIs	https://doi.org/10.1016/j.amc.2011.02.033
State	Published - 15 May 2011

Keywords

Adjacency matrix
Lower bound
Spectral radius
Upper bound
Weighted graph

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10.1016/j.amc.2011.02.033

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title = "Extremal graph characterization from the bounds of 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 a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained.",

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

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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 a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained.

KW - Adjacency matrix

KW - Lower bound

KW - Spectral radius

KW - Upper bound

KW - Weighted graph

UR - https://www.scopus.com/pages/publications/79953197198

U2 - 10.1016/j.amc.2011.02.033

DO - 10.1016/j.amc.2011.02.033

M3 - Article

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EP - 7426

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 18

ER -

Extremal graph characterization from the bounds of the spectral radius of weighted graphs

Abstract

Keywords

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