期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2005
卷号：2005
DOI：10.1155/IJMMS.2005.1565
出版社：Hindawi Publishing Corporation
摘要：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)=∑j=0[n/2](−1)jp(G,j)xn−2j, called the matching polynomial of G, is closely related to the Hosoya index introduced in applications in physics and chemistry. In this work we generalize this polynomial by introducing the number of
disjoint paths of length t, denoted by pt(G,j). We compare this higher-order matching polynomial with the usual one,
establishing similarities and differences. Some interesting examples are given. Finally, connections between our generalized matching polynomial and hypergeometric functions are found.
