| 摘要: |
| 本文研究了边连通度为r的n阶连通图中距离谱半径最小的极图问题.利用组合的方法,确定了K(n-1,r)为唯一的极图,其中K(n-1,r)是由完全图Kn-1添加一个顶点v以及连接v与Kn-1中r个顶点的边所构成.上述结论推广了极图理论中的相关结果. |
| 关键词: 图 距离矩阵 谱半径 边连通度 |
| DOI： |
| 分类号:O157.5 |
| 基金项目:Supported by National Natural Science Foundation of China (11071002);Program for New Century Excellent Talents in University,Key Project of Chinese Ministry of Education (210091);Natural Science Research Foundation of Department of Education of Anhui Province (KJ2013A196). |
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| MINIMUM DISTANCE SPECTRAL RADIUS OF GRAPHS WITH GIVEN EDGE CONNECTIVITY |
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LI Xiao-xin1,2, FAN Yi-zheng2, WANG Yi2
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1.Department of Mathematics and Computer Sciences, Chizhou University, Chizhou 247000, China;2.School of Mathematical Sciences, Anhui University, Hefei 230601, China
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| Abstract: |
| In this paper we study the extremal graphs with minimum distance spectral radius among all connected graphs of order n and edge connectivity r.By using the combinatorial method,we determine that K(n-1,r) is the unique extremal graph,where K(n-1,r) is obtained from the complete graph Kn-1 by adding a vertex v together with edges joining v to r vertices of Kn-1.All the above generalize the related results of the extremal graph theory. |
| Key words: graph distance matrix spectral radius edge connectivity |
