Remoteness and distance eigenvalues of a graph

Huiqiu Lin; Kinkar Ch Das; Baoyindureng Wu

doi:10.1016/j.dam.2016.07.018

Remoteness and distance eigenvalues of a graph

Huiqiu Lin, Kinkar Ch Das, Baoyindureng Wu

Department of Mathematics

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

17 Scopus citations

Abstract

Let G be a connected graph of order n with diameter d. Remoteness ρ of G is the maximum average distance from a vertex to all others and ∂₁≥⋯≥∂_n are the distance eigenvalues of G. Aouchiche and Hansen (0000), Aouchiche and Hansen conjectured that ρ+∂₃>0 when d≥3 and ρ+∂_⌊7d8⌋>0. In this paper, we confirm these two conjectures. Furthermore, we give lower bounds on ∂_n+ρ and ∂₁−ρ when G≇K_n and the extremal graphs are characterized.

Original language	English
Pages (from-to)	218-224
Number of pages	7
Journal	Discrete Applied Mathematics
Volume	215
DOIs	https://doi.org/10.1016/j.dam.2016.07.018
State	Published - 31 Dec 2016

Keywords

Distance eigenvalues
Distance matrix
Remoteness

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10.1016/j.dam.2016.07.018

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title = "Remoteness and distance eigenvalues of a graph",

abstract = "Let G be a connected graph of order n with diameter d. Remoteness ρ of G is the maximum average distance from a vertex to all others and ∂1≥⋯≥∂n are the distance eigenvalues of G. Aouchiche and Hansen (0000), Aouchiche and Hansen conjectured that ρ+∂3>0 when d≥3 and ρ+∂⌊7d8⌋>0. In this paper, we confirm these two conjectures. Furthermore, we give lower bounds on ∂n+ρ and ∂1−ρ when G≇Kn and the extremal graphs are characterized.",

keywords = "Distance eigenvalues, Distance matrix, Remoteness",

author = "Huiqiu Lin and Das, \{Kinkar Ch\} and Baoyindureng Wu",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2016",

month = dec,

day = "31",

doi = "10.1016/j.dam.2016.07.018",

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T1 - Remoteness and distance eigenvalues of a graph

AU - Lin, Huiqiu

AU - Das, Kinkar Ch

AU - Wu, Baoyindureng

PY - 2016/12/31

Y1 - 2016/12/31

N2 - Let G be a connected graph of order n with diameter d. Remoteness ρ of G is the maximum average distance from a vertex to all others and ∂1≥⋯≥∂n are the distance eigenvalues of G. Aouchiche and Hansen (0000), Aouchiche and Hansen conjectured that ρ+∂3>0 when d≥3 and ρ+∂⌊7d8⌋>0. In this paper, we confirm these two conjectures. Furthermore, we give lower bounds on ∂n+ρ and ∂1−ρ when G≇Kn and the extremal graphs are characterized.

AB - Let G be a connected graph of order n with diameter d. Remoteness ρ of G is the maximum average distance from a vertex to all others and ∂1≥⋯≥∂n are the distance eigenvalues of G. Aouchiche and Hansen (0000), Aouchiche and Hansen conjectured that ρ+∂3>0 when d≥3 and ρ+∂⌊7d8⌋>0. In this paper, we confirm these two conjectures. Furthermore, we give lower bounds on ∂n+ρ and ∂1−ρ when G≇Kn and the extremal graphs are characterized.

KW - Distance eigenvalues

KW - Distance matrix

KW - Remoteness

UR - https://www.scopus.com/pages/publications/84991039870

U2 - 10.1016/j.dam.2016.07.018

DO - 10.1016/j.dam.2016.07.018

M3 - Article

AN - SCOPUS:84991039870

SN - 0166-218X

VL - 215

SP - 218

EP - 224

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Remoteness and distance eigenvalues of a graph

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Keywords

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