A lower bound for the spectral radius of graphs with fixed diameter

S.M. Cioaba, E.R. van Dam, J.H. Koolen, J.H. Lee

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Abstract

We determine a lower bound for the spectral radius of a graph in terms of the number of vertices and the diameter of the graph. For the specific case of graphs with diameter three we give a slightly better bound. We also construct families of graphs with small spectral radius, thus obtaining asymptotic results showing that the bound is of the right order. We also relate these results to the extremal degree/diameter problem.
Original languageEnglish
Pages (from-to)1560-1566
JournalEuropean Journal of Combinatorics
Volume31
Issue number6
Publication statusPublished - 2010

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Spectral Radius
Lower bound
Graph in graph theory

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Cioaba, S.M. ; van Dam, E.R. ; Koolen, J.H. ; Lee, J.H. / A lower bound for the spectral radius of graphs with fixed diameter. In: European Journal of Combinatorics. 2010 ; Vol. 31, No. 6. pp. 1560-1566.
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A lower bound for the spectral radius of graphs with fixed diameter. / Cioaba, S.M.; van Dam, E.R.; Koolen, J.H.; Lee, J.H.

In: European Journal of Combinatorics, Vol. 31, No. 6, 2010, p. 1560-1566.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - A lower bound for the spectral radius of graphs with fixed diameter

AU - Cioaba, S.M.

AU - van Dam, E.R.

AU - Koolen, J.H.

AU - Lee, J.H.

N1 - Appeared earlier as CentER Discussion Paper 2008-75

PY - 2010

Y1 - 2010

N2 - We determine a lower bound for the spectral radius of a graph in terms of the number of vertices and the diameter of the graph. For the specific case of graphs with diameter three we give a slightly better bound. We also construct families of graphs with small spectral radius, thus obtaining asymptotic results showing that the bound is of the right order. We also relate these results to the extremal degree/diameter problem.

AB - We determine a lower bound for the spectral radius of a graph in terms of the number of vertices and the diameter of the graph. For the specific case of graphs with diameter three we give a slightly better bound. We also construct families of graphs with small spectral radius, thus obtaining asymptotic results showing that the bound is of the right order. We also relate these results to the extremal degree/diameter problem.

M3 - Article

VL - 31

SP - 1560

EP - 1566

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

SN - 0195-6698

IS - 6

ER -