The A_{\alpha}-Spectral Radius and Fractional Matchings in Graphs

A fractional matching of a graph G is a function f that assigns to each edge a value in, is defined as the maximum value of e∈E(G) f (e) taken over all fractional matchings of G.This paper investigates the relationship between the fractional matching number of a graph and the spectral radius of its A α -matrix.Several sufficient conditions are also established, expressed in terms of the A α -spectral radii of a graph and its complement, which guarantee the existence of a fractional perfect matching.