Abstract
ABSTRACTA fractional matching of a graph G is a function f giving each edge a number in so that for each , where is the set of edges incident to v. The fractional matching number of G, written , is the maximum of 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.
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