范益政,李双东,谭莹莹.双圈图的Laplace谱跨度[J].数学研究及应用,2010,30(1):17~28
双圈图的Laplace谱跨度
The Laplacian Spread of Bicyclic Graphs
投稿时间:2008-02-17  最后修改时间:2008-10-06
DOI:10.3770/j.issn:1000-341X.2010.01.002
中文关键词:  双圈图  Laplace 矩阵  跨度.
英文关键词:bicyclic graph  Laplacian matrix  spread.
基金项目:国家自然科学基金(Grant No.10601001),安徽省自然科学基金(Grant No.070412065),安徽省青年教师科研资助项目(Grant No.2008jql083),安徽省教育厅自然科学研究项目(Grant No.2005kj005zd),安徽大学学术带头人资助项目,安徽大学基础数学创新团队资助项目.
作者单位
范益政 安徽大学数学科学学院, 安徽 合肥 230039 
李双东 安徽大学数学科学学院, 安徽 合肥 230039 
谭莹莹 安徽建筑工业学院数理系, 安徽 合肥 230022 
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中文摘要:
      图的Laplace谱跨度定义为图的Laplace矩阵的最大特征值和次小特征值之差.在最近的工作中, 我们已经确定了具有极大谱跨度的树和单圈图.本文我们继续讨论图的谱跨度, 证明了具有极大谱跨度的双圈图恰有两个, 分别是由星图在其悬挂点之间添加两条关联的边和添加两条不关联的边而得到.
英文摘要:
      The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In our recent work, we have determined the graphs with maximal Laplacian spreads among all trees of fixed order and among all unicyclic graphs of fixed order, respectively. In this paper, we continue the work on Laplacian spread of graphs, and prove that there exist exactly two bicyclic graphs with maximal Laplacian spread among all bicyclic graphs of fixed order, which are obtained from a star by adding two incident edges and by adding two nonincident edges between the pendant vertices of the star, respectively.
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