The trees with the second smallest normalized Laplacian eigenvalue at least

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• 作者：Xiaoguo Tian ^{xiaoguotianwycm@163.com} ; Ligong Wang ; ^{lgwangmath@163.com}
• 关键词：Second smallest normalized Laplacian eigenvalue ; Tree
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：31 March 2017
• 年：2017
• 卷：220
• 期：Complete
• 页码：118-133
• 全文大小：617 K
• 卷排序：220

文摘

Let λ2(G)λ2(G) be the second smallest normalized Laplacian eigenvalue of a graph GG. In this paper, we determine all trees with λ2(T)≥1−32. Meanwhile, if TT is a tree of diameter 66, then we prove that λ2(T)≤1−32. Moreover, we determine all trees of diameter d=3d=3 or 66 with λ2(T)=1−32.