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arXiv · 1905.06557

Signless Laplacian spectral radius and fractional matchings in graphs

Yingui Pan·Jianping Li
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Abstract

A fractional matching of a graph $G$ is a function $f$ giving each edge a number in $[0,1]$ such that $\sum_{e\inΓ(v)}f(e)\leq1$ for each vertex $v\in V(G)$, where $Γ(v)$ is the set of edges incident to $v$. The fractional matching number of $G$, written $α^{\prime}_*(G)$, 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.

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Yingui Pan, Jianping Li. 2019-05-27. Signless Laplacian spectral radius and fractional matchings in graphs. https://arxiv.org/abs/1905.06557

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