期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

给定染色数的无符号Laplace谱半径(英文) 被引量：6

The Signless Laplacian Spectral Radius of Graphs with Given Chromatic Number
下载PDF
导出
摘要 设Gkn(k≥2)为n阶的染色数为k的连通图的集合.本文确定了Gnk中具有极大无符号Laplace谱半径的图,即k =2时为完全二部图,k≥3时为Turán图.本文也讨论了Gnk中的具有极小无符号Laplace谱半径的图,对k≤3的情形给出了此类图的刻画. Let （k ≥ 2） be the set of all connected graphs of order n with chromatic number k. We determine the graphs with maximal signless Laplacian spectral radius among all graphs in , namely complete bipartite graphs for k = 2 and Turin graph for k ≥ 3. We also consider the graphs with minimal signless Laplacian spectral radius in , and characterized such graphs for k ≤3.
作者 蔡改香 范益政
机构地区 安徽大学数学科学学院 安庆师范学院数学与计算科学学院
出处 《应用数学》 CSCD 北大核心 2009年第1期161-167,共7页 Mathematica Applicata
基金 Supported by National Natural Science Foundation of China(10601001) Anhui Provincial Natural Science Foundation(050460102 ,070412065) NSF of Depart ment of Education of Anhui Province (2005kj005zd) Foundation of Innovation Teamon Basic Mathematics of Anhui University Foundation of Talents Group Construction of Anhui University .
关键词 图 染色数 无符号Laplace谱半径 Graph Chromatic number Signless Laplaeian spectral radius
分类号 O157.5 [理学—基础数学] O151.21 [理学—基础数学]
  • 相关文献

参考文献1

二级参考文献9

  • 1Biggs,N.L.,Algebraic GraphTheory,Second Edition,Cambridge University Press,Cambridge,1993.
  • 2Bondy,J.A.,Murty,U.S.R.,Graph Theory with Applications,North Holland,New York,1976.
  • 3Hoffman,A.J.,Some recent results on spectral properties of graphs,In:H.Sachs,H.J.Voss,H.Walther,eds.,Beitrage ZurGraphentheorie,Int.Koll.Manebach,Leipzig,1968,75-80.
  • 4Doob,M.,An interrelation between line graphs,eigenvalues and matrix,Journal ofCombin.Theory Ser.B.,1973,15:40-50.
  • 5Cvetkovic,D.,Doob,M.,Sachs,H.,Spectra of Graphs,Theory and Application,AcademicPress,New York,1980.
  • 6Fiedler,M.,Algebraic connectivity of graphs,Czechoslovak Math.J.,1973,23:298-305.
  • 7Mohar,B.,The Laplacian Spectrum of Graphs,in GraphTheory,In:Y.Alvia,G.Chartrand,O.R.Ollermann,et al.eds.,Combinatorics andApplications,Wiley-Interscience,New York,1991,871-898.
  • 8Merris,R.,Laplacian matrices of graphs:A survey,Linear Algebra andApplications,1994,197/198:143-176.
  • 9Desai,M.,Rao,V.,A characterization of the smallest eigenvalue of a graph,Journal ofGraph Theory,1994,18(2):181-194.

共引文献8

同被引文献24

  • 1YU A,TIAN F.On the spectral radius of bicyclic graphs[J].Match Commun Math Comput Chem,2004,52:91-101.
  • 2ZHAI M Q,WU Y R,SHU J L.Maximizing the spectral radius of bicyclic graphs with fixed girth[J].Linear Algebra and its Applications,2009,431:716-723.
  • 3CVETKOVI(C)D,DOOB M,SACHS H.Spectra of Graphs[M].3rd ed.Heidelberg:Johann Ambrosius Barth Verlag,1995.
  • 4BRUALDI R A,SOLHEID E S.On the spectral radius of complementary acyclic matrices of zeros and ones[J].SIAM J Algebra Discrete Methods,1986,7(2):265-272.
  • 5VAN DAM E R,HAEMERS W.Which graphs are determined by theirspectrum[J].Linear Algebra and itsApplications,2003,373:241-272.
  • 6CVETKOVI(C)D,ROWLINSON P,SIMI(C) S.Signless Laplacian of finite graphs[J].Linear Algebra and its Applications,2007,423:155-171.
  • 7CVETKOVI(C)D,SIMI(C) S K.Towards a spectral theory of graphs based on the signless Laplacian:Ⅰ[J].Publications de L'Institut Mathematique Nouvelle série tome,2009,85(99):1-15.
  • 8[8[CVETKOVI(C)D,SIMI(C) S K.Towards a spectraltheory of graphs based on the signless Laplacian:Ⅱ[J].Linear Algebra and its Applications,2010,432(9):2257-2272.
  • 9CVETKOVI(C)D,SIMI(C) S K.Towards a spectral theory of graphs based on the signless Laplacian:Ⅲ[J].Applicable Analysis and Discrete Mathematics,2010,4:156-166.
  • 10FAN Y Z,TAM B S,ZHOU J.Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order[J].Linear Multilinear Algebra,2008,56(4):381-397.

引证文献6

二级引证文献4

应用数学
2009年 第1期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部