Sharp upper bounds on the second largest eigenvalues of connected graphs

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• 作者：Mingqing Zhai^a ; ^{mqzhai@chzu.edu.cn} ; Huiqiu Lin^b ; ^{huiqiulin@126.com} ; Bing Wang^a ; ^{wuyuwuyou@126.com}
• 关键词：05C50
• 刊名：Linear Algebra and its Applications
• 出版年：2012
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：1 July, 2012
• 卷：437
• 期：1
• 页码：236-241
• 文件大小：280 K

摘要

Let be the second largest eigenvalue of a graph. Powers (1988) gave some upper bounds of for general graphs and bipartite graphs, respectively. Considering that these bounds are not always attainable for connected graphs, we present sharp upper bounds of for connected graphs and connected bipartite graphs in this paper. Moreover, the extremal graphs are completely characterized.