无符号拉普拉斯谱半径与分数完美匹配
The Signless Laplace Spectral Radius and Fractional Perfect Matching
DOI: 10.12677/AAM.2022.119709, PDF,   
作者: 李 振, 章 超*：贵州大学，数学与统计学院，贵州 贵阳
关键词: 匹配理论；谱理论；商矩阵；Matching Theory； Spectral Theory； Quotient Matrix
摘要: 图G的分数完美匹配是一个函数f，为每条边从[0, 1]中赋值，使得对于任意的ν∈V(G)均有，其中τ(ν)是邻接于顶点v的所有边的集合。近年来，许多研究关注谱理论和匹配理论之间的联系，并利用无符号拉普拉斯谱半径给出了完美匹配存在的充分条件。作为这一结果的延伸，本文研究了无符号拉普拉斯谱的下界，以确保图G中存在分数完美匹配。令r(n)为方程X3+(5-3n)X2+(2n2-5n)x-2n2+10n-12=0的最大根，对于n≥4，当q1(G)＞r(n)时，图G具有分数完美匹配，其中q1(G)表示图G的无符号拉普拉斯谱半径。
Abstract: A fractional perfect matching of a graph G is a function f giving each edges a number [0, 1], so that for each ν∈V(G) , where τ(ν) is the set of edges incident to v. In recent years, many studies have focused on the connection between spectral theory and matching theory, and have given sufficient conditions for the existence of perfect matching using signless Laplacian spec-tral radius. As an extension of this result, in this paper, we study the lower bound on signless Lapla-cian spectrum to ensure the existence of a fractional perfect matching in graphs. Let r(n) be the largest root of equation X3+(5-3n)X2+(2n2-5n)x-2n2+10n-12=0 . For n≥4 , if q1(G)＞r(n) , then G has a fractional perfect matching, where q1(G) is the signless Laplacian spectral radius of the graph G.
文章引用：李振, 章超. 无符号拉普拉斯谱半径与分数完美匹配[J]. 应用数学进展, 2022, 11(9): 6694-6699. https://doi.org/10.12677/AAM.2022.119709

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