Abstract
A 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 vertex v∈V(G), where Γ(v) is the set of edges incident to v. The fractional matching number of G, written α∗′(G), is the maximum value of ∑e∈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 conditions for the existence of a fractional perfect matching of a graph in terms of the signless Laplacian spectral radius of the graph and its complement.
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