Solutions to unsolved problems on the minimal energies of two classes of trees

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• 作者：Yongqiang Bai ^{bmbai@163.com" class="auth_mail" title="E-mail the corresponding author} ; Hongping Ma ; ^{hpma@163.com" class="auth_mail" title="E-mail the corresponding author} ; ^{mahp@jsnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Minimal energy ; Tree ; Pendent vertex ; Diameter
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：5 August 2016
• 年：2016
• 卷：286
• 期：Complete
• 页码：49-56
• 全文大小：360 K

文摘

The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. Let T_n,p,${\mathbb{T}}_{n,p},$T_n,d${\mathcal{T}}_{n,d}$ be the set of all trees of order n with p pendent vertices, diameter d  , respectively. In this paper, we completely characterize the trees with second-minimal and third-minimal energy in T_n,p${\mathbb{T}}_{n,p}$ (T_n,d,${\mathcal{T}}_{n,d},$ respectively) for 4≤p≤n−9$4\le p\le n-9$ (10≤d≤n−3,$10\le d\le n-3,$ respectively), which solves the problems left in Ma (2014).