华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (3): 73-84.

• 应用数学与基础数学 • 上一篇    下一篇

给定独立数的双圈图的最大拟拉普拉斯谱半径

李瑞林;施劲松;董炳灿   

  1. 华东理工大学 数学系, 上海 200237
  • 收稿日期:2010-09-01 修回日期:2010-12-01 出版日期:2011-05-25 发布日期:2011-05-25
  • 通讯作者: 施劲松

Maximal signless Laplacian spectral radius of bicyclic graphs with given independence number

LI Rui-lin; SHI Jin-song; DONG Bing-can   

  1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
  • Received:2010-09-01 Revised:2010-12-01 Online:2011-05-25 Published:2011-05-25
  • Contact: SHI Jin-song

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摘要： 设B(n,α)是独立数为α的n阶双圈图, B1(n,α)是由B(n,α)中含有两个边不交的圈构成的双圈图子集, B2(n,α) = B(n,α)\B1(n,α). 文中分别研究了B1(n,α)和B2(n,α)中具有最大拟拉普拉斯谱半径的极图. 进一步地, 得到了B(n,α)中拟拉普拉斯谱半径的上界, 并给出达到上界的极图.

关键词: 拟拉普拉斯谱半径, 双圈图, 独立数, 拟拉普拉斯谱半径, 双圈图, 独立数

Abstract: Let B(n,α) be the class of bicyclic graphs on n vertices with independence numberα. Let B1(n,α) be the subclass of B(n,α) consisting of all bicyclic graphs with two edge-disjoint cycles and B2(n,α) = B（n,α)\B1(n,α). This paper determined the unique graph with the maximal signless Laplacian spectral radius among all graphs in B1(n,α) and B2(n,α), respectively. Furthermore, the upper bound of the signless Laplacian spectral radius and the extremal graph for B(n,α) were also obtained.

Key words: bicyclic graph, independence number, signless Laplacian spectral radius, bicyclic graph, independence number

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