华东师范大学学报(自然科学版) ›› 2005, Vol. 2005 ›› Issue (4): 6-11,9.

• 数学 统计学 • 上一篇    下一篇

双圈图的最大与最小特征值

尹书华1,3, 束金龙1,2*   

  1. 1. 华东师范大学数学系, 上海200062; 2.华东师范大学地理信息科学教育部重点实验室，上海200062; 3. 浙江万里学院数学研究所,浙江宁波315100
  • 收稿日期:2003-11-07 修回日期:2003-12-17 出版日期:2005-11-25 发布日期:2005-11-25
  • 通讯作者: 束金龙

The Largest and Smallest Eigenvalues of Double Cyclic Graphs(Chinese)

YIN Shu-hua 1,3 , SHU Jin-long 1,2   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China; 2.Key Laboratory of Geographic Information Science, Ministry of Education, East China Normal University, Shanghai 200062,China}; 3. Institute of Mathematics, Zhejiang Univeristy, Ningbo 315100,Zhejiang, China
  • Received:2003-11-07 Revised:2003-12-17 Online:2005-11-25 Published:2005-11-25
  • Contact: SHU Jin-long

摘要： 讨论了双圈图的最大和最小特征值,给出了其最大特征值随圈上点的变化关系; 讨论了双圈图的最小特征值的下界; 当n≥18时双圈图中最小特征值达到最小的极图为Sn(3,3). 在此基础上给出了双圈图谱展的上界.

关键词: 双圈图, 偶图, 谱展, 双圈图, 偶图, 谱展

Abstract: Two classes of connected double cyclic graphs, An(p,q) and Bn(Gls,Gkt,Tm), are investigated in this paper. The relationship between the largest eigenvalues and the girths, and low bounds of the smallest eigenvalues of the graphs are obtained.Moreover, extremal graphs with these bounds are characterized,respectively, and the upper bound on the spread of the graphs is presented.

Key words: bipartite graph, spread, double cyclic graph, bipartite graph, spread

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