The Higher-Order Matching Polynomial of a Graph

ABSTRACT: Given a graph G with n vertices, let p(G, j) denote the number of ways j mutually nonincident edges can be selected in G. The polynomial M(x) = [n/2] j=0 (−1)j p(G, j)xn−2j, called the matching polynomial of G, is closely related to the Hosoya index introduced in applications in physics an...