Signless Laplacian spectral radius and fractional matchings in graphs

2017/11/07 by Liu, Ruifang, Lu, Yu · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.02310

Abstract

A \it fractional matching of a graph G is a function f giving each edge a number in [0,1] so that ∑_{e∈ Γ(v)}f(e)≤ 1 for each v∈ V(G), where Γ(v) is the set of edges incident to v. The \it fractional matching number of G, written α'_*(G), is the maximum of ∑_{e∈ E(G)}f(e) over all fractional matchings f. In this paper, we propose the relations between the fractional matching number and the signless Laplacian spectral radius of a graph. As applications, we also give sufficient spectral conditions for existence of a fractional perfect matching in a graph in terms of the signless Laplacian spectral radius of the graph and its complement.

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