On the theory of the matching polynomial
Abstract In this paper we report on the properties of the matching polynomial α( G ) of a graph G . We present a number of recursion formulas for α( G ), from which it follows that many families of orthogonal polynomials arise as matching polynomials of suitable families of graphs. We consider the relation between the matching and characteristic polynomials of a graph. Finally, we consider results which provide information on the zeros of α( G ).