Spectral radius and degree sequence of a graph

Chia An Liu; Chih-wen Weng

doi:10.1016/j.laa.2012.12.016

Spectral radius and degree sequence of a graph

Chia An Liu^*, Chih-wen Weng

^*Corresponding author for this work

Department of Applied Mathematics

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

15 Scopus citations

Abstract

Let G be a simple connected graph of order n with degree sequence d ₁,d₂,⋯,d_n in non-increasing order. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer ℓ at most n, we give a sharp upper bound for ρ(G) by a function of d₁,d₂,⋯,d _ℓ, which generalizes a series of previous results.

Original language	English
Pages (from-to)	3511-3515
Number of pages	5
Journal	Linear Algebra and Its Applications
Volume	438
Issue number	8
DOIs	https://doi.org/10.1016/j.laa.2012.12.016
State	Published - 2013

Keywords

Adjacency matrix
Degree sequence
Graph
Spectral radius

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10.1016/j.laa.2012.12.016

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abstract = "Let G be a simple connected graph of order n with degree sequence d 1,d2,⋯,dn in non-increasing order. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer ℓ at most n, we give a sharp upper bound for ρ(G) by a function of d1,d2,⋯,d ℓ, which generalizes a series of previous results.",

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T1 - Spectral radius and degree sequence of a graph

AU - Liu, Chia An

AU - Weng, Chih-wen

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N2 - Let G be a simple connected graph of order n with degree sequence d 1,d2,⋯,dn in non-increasing order. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer ℓ at most n, we give a sharp upper bound for ρ(G) by a function of d1,d2,⋯,d ℓ, which generalizes a series of previous results.

AB - Let G be a simple connected graph of order n with degree sequence d 1,d2,⋯,dn in non-increasing order. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer ℓ at most n, we give a sharp upper bound for ρ(G) by a function of d1,d2,⋯,d ℓ, which generalizes a series of previous results.

KW - Adjacency matrix

KW - Degree sequence

KW - Graph

KW - Spectral radius

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U2 - 10.1016/j.laa.2012.12.016

DO - 10.1016/j.laa.2012.12.016

M3 - Article

AN - SCOPUS:84875427189

SN - 0024-3795

VL - 438

SP - 3511

EP - 3515

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 8

ER -

Spectral radius and degree sequence of a graph

Abstract

Keywords

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