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Signless Laplacian spectral radius and fractional matchings in graphs
Discrete Mathematics ( IF 0.8 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.disc.2020.112016
Yingui Pan , Jianping Li , Wei Zhao

A fractional matching of a graph $G$ is a function $f$ giving each edge a number in $[0,1]$ such that $\sum_{e\in\Gamma(v)}f(e)\leq1$ for each vertex $v\in V(G)$, where $\Gamma(v)$ is the set of edges incident to $v$. The fractional matching number of $G$, written $\alpha^{\prime}_*(G)$, is the maximum value of $\sum_{e\in E(G)}f(e)$ over all fractional matchings. In this paper, we investigate the relations between the fractional matching number and the signless Laplacian spectral radius of a graph. Moreover, we give some sufficient spectral conditions for the existence of a fractional perfect matching.

中文翻译:

图中的无符号拉普拉斯谱半径和分数匹配

图 $G$ 的分数匹配是一个函数 $f$ 给每条边一个 $[0,1]$ 中的数字,使得 $\sum_{e\in\Gamma(v)}f(e)\leq1$对于每个顶点 $v\in V(G)$,其中 $\Gamma(v)$ 是与 $v$ 相关的边的集合。$G$的小数匹配数,写成$\alpha^{\prime}_*(G)$,是$\sum_{e\in E(G)}f(e)$在所有小数上的最大值匹配。在本文中,我们研究了分数匹配数与图的无符号拉普拉斯谱半径之间的关系。此外,我们为分数完美匹配的存在给出了一些充分的谱条件。
更新日期:2020-10-01
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