3类图完美匹配的数目

摘要

It is an interesting and important problem that count the number of the perfect matchings in graphs, since it origins from both physics and chemistry. But the problem of counting the number of the perfect matchings for general graphs is NP-difficult. In this paper, by applying differentiation, summation and re-recursion, the several counting formulas of the perfect matching for three specific types of graphs are given.%图的完美匹配计数问题是匹配理论研究中的一个重要课题,此问题有很强的物理学和化学背景.但是,一般图的完美匹配计数问题却是NP-困难的.用划分、求和、再递推的方法给出了三类特殊图完美匹配数目的计算公式.