文献类型：期刊文献

英文题名：The second largest algebraic connectivity of trees with fixed diameter

作者：Yang, Yi-Chen[1];Guo, Ji-Ming[1]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China

年份：2026

卷号：45

期号：7

外文期刊名：COMPUTATIONAL & APPLIED MATHEMATICS

收录：;EI(收录号：20261320339467);WOS:【SCI-EXPANDED(收录号:WOS:001714735500002)】；

基金：This work is supported by NSFC (No. 12171154).

语种：英文

外文关键词：Laplacian matrix; Algebraic connectivity; Tree; Diameter

摘要：The algebraic connectivity of G is the second smallest eigenvalue of its Laplacian matrix. Let T(n,d)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathscr {T}(n, d) $$\end{document} denote the set of all trees with n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ n $$\end{document} vertices and diameter d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ d $$\end{document}. In this paper, we identify the trees in T(n,d)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathscr {T}(n, d)$$\end{document} that achieve the second largest algebraic connectivity when d is odd. If d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ d $$\end{document} is even, a conjecture about which trees achieve the second largest algebraic connectivity is also proposed.