On the matching polynomials of graphs with small number of cycles of even length

摘要

Suppose that G is a simple graph. We prove that if G contains a small number of cycles of even length then the matching polynomial of G can be expressed in terms of the characteristic polynomials of the skew adjacency matrix A(G(e)) of an arbitrary orientation G(e) of G and the minors of A(G(e)). In addition to a formula previously discovered by Godsil and Gutman, we obtain a different formula for the matching polynomial of a general graph. (c) 2005 Wiley Periodicals, Inc.