Fractional matching number and eigenvalues of a graph

A fractional matching of a graph G is a function f giving each edge a number in [0, 1] so that Sigma(e is an element of e(v)) f (e) = 1 for each v. V(G), where (v) is the set of edges incident to v. The fractional matching number of G, written. * (G), is the maximum of Sigma(e is an element of e).E(G) f (e) over all fractional matchings. In this paper, we study the connections between the fractional matching number and the Laplacian spectral radius of a graph. We also give some sufficient spectral conditions for the existence of a fractional perfect matching.