The Laplacian spectral radius of trees and maximum vertex degree - Details

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author：

Yuan, X.-Y. (Yuan, X.-Y..) ^[1] | Liu, Y. (Liu, Y..) ^[2] | Han, M. (Han, M..) ^[3]

Indexed by：

Scopus

Abstract：

Let　Δ(T)　and　μ(T)　denote　the　maximum　degree　and　the　Laplacian　spectral　radius　of　a　tree　T,　respectively.　In　this　paper　we　prove　that　for　two　trees　T1　and　T2　on　n(n≥21)　vertices,　if　Δ(　T　1)>Δ(　T2)　and　Δ(　T1)≥11n/　30⌉+1,　then　μ(　T1)>μ(　T2),　and　the　bound　＂Δ(　T1)<11n/30⌉+1＂　is　the　best　possible.　We　also　prove　that　for　two　trees　T1　and　T2　on　2k(k≥4)　vertices　with　perfect　matchings,　if　Δ(　T1)>Δ(　T　2)　and　Δ(　T1)≥k/2⌉+2,　then　μ(　T　1)>μ(　T2).　©　2011　Elsevier　B.V.　All　rights　reserved.

Keyword：

Laplacian spectral radius; Maximum degree; Tree

Community：

[ 1 ] [Yuan, X.-Y.]Department of Mathematics, Shanghai University, Shanghai, 200444, China
[ 2 ] [Liu, Y.]College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350108, China
[ 3 ] [Han, M.]Department of Mathematics, Shanghai University, Shanghai, 200444, China

Reprint 's Address：

[Yuan, X.-Y.]Department of Mathematics, Shanghai University, Shanghai, 200444, China

Email：

xiyingyuan2007@hotmail.com

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Source ：

Discrete Mathematics

ISSN： 0012-365X

Year： 2011

Issue： 8-9

Volume： 311

Page： 761-768

0 . 5 1 9

JCR@2011

0 . 7 0 0

JCR@2023

JCR Journal Grade：3

CAS Journal Grade：4

Cited Count：

WoS CC Cited Count： 0

SCOPUS Cited Count： 5

ESI Highly Cited Papers on the List： 0 Unfold All

WanFang Cited Count：

Chinese Cited Count：

30 Days PV： 1

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