4类图完美匹配数目的显式表达式

摘要

Matching counting theory is at the core of graph theory, since it is origins from both physics, computer science and chemistry. But the problem of counting the number of perfect matching for general graphs is NP-hard. By applying differentia-tion, summation and re-nested recursive calculation, several counting formulas of the perfect matching for four specific types of graphs are given. By the presented method, the number of all perfect matching of many graphs that the same structure is repeated can be calculated.%匹配计数理论是图论的核心内容之一，此问题有很强的物理学、计算机科学和化学背景；但是，一般图的完美匹配计数问题却是NP-难问题。用划分、求和、再嵌套递推的方法给出了4类图完美匹配数目的显式表达式；所给出的方法，可以计算出相同结构重复出现的许多图的所有完美匹配的数目。