Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In graph theory and combinatorics, both fields within mathematics, a matching polynomial (sometimes called an acyclic polynomial) is a generating function of the numbers of matchings of various sizes in a graph. Several different types of matching polynomials have been defined. Let G be a graph with n vertices and let mk be the number of k-edge matchings. The first type of matching polynomial is a direct generalization of the rook polynomial. The second type of matching polynomial has remarkable connections with orthogonal polynomials. For instance, if G = Km,n, the complete bipartite graph, then the second type of matching polynomial is related to the generalized Laguerre polynomial Ln (x).

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