一类3-正则图完美对集的计数

图的完美对集计数理论是图论研究的重要内容之一,此问题的研究具有很强的计算机科学、物理学和化学的应用背景,是一个有生机和活力的研究领域,也是快速发展的组合数学理论中许多重要思想的源泉.构造了一类3-正则新图2-3-nC_6,用嵌套递推的方法,得到了图2-3-nC_6的完美对集数的一个递推关系,再解出这个递推式的通解,从而得到了这个图的完美对集数计算公式.最后又给出这个图完美对集数计算公式的一个组合证明.

Enumeration of perfect matchings of a type of 3-regular graphs

The perfect matching counting theory of graphs is one of the important contents of graph theory research. The research of this problem has a strong application background in computer science, physics and chemistry. It is a field of activity and vitality, and it is also the source of many important ideas in fast developing combinatorial mathematics. A new type of 3-regular graph 2-3-nC6 is constructed. Using the nested recursive method, a recursive relationship for the number of perfect matchings of graph 2-3-nC6 is obtained. By solving the general solution of the recursive formula, the formula for calculating the number of perfect matchings in this graph is given. Finally, a combined proof of the formula for calculating the number of perfect matchings in this graph is provided.