文献类型：期刊文献

英文题名：Fractional Matchings in Graphs from the Spectral Radius

作者：Chen, Qian-Qian[1];Guo, Ji-Ming[1];Wang, Zhiwen[1]

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

年份：2024

卷号：47

期号：4

外文期刊名：BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001228655100003)】；

基金：No Statement Available

语种：英文

外文关键词：Fractional matching number; Spectral radius; Graph; Matching number

摘要：Denote by Gn,nu & lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {G}_{n, \nu <^>*}$$\end{document}(Gn,nu & lowast;& lowast;)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathcal {G}<^>*_{n,\nu <^>*})$$\end{document} the collection of all (connected) graphs of order n having a fractional matching number nu & lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu <^>*$$\end{document}. This paper characterizes the graphs in Gn,nu & lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {G}_{n,\nu <^>*}$$\end{document} and Gn,nu & lowast;& lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {G}<^>*_{n,\nu <^>*}$$\end{document} with the maximum spectral radius, and establishes a lower bound for the spectral radius of graphs of order n to guarantee that their fractional matching numbers are at least tau+12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau +\frac{1}{2}$$\end{document}. In addition, we explore the relationship between the spectral radius, perfect matching and fractional perfect matching of G. Moreover, we present a spectral condition guaranteeing that the matching number of a graph is at least k+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k+1$$\end{document}, which generalizes some previous known results.