一类3-正则图完美对集的计数  

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

作　　者：唐保祥[1] 任韩[2] TANG Baoxiang;REN Han(School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China;Department of Mathematics, East China Normal University, Shanghai 200062, China)

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001 [2]华东师范大学数学系,上海200062

出　　处：《大连理工大学学报》2020年第4期437-440,共4页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(11171114)。

摘　　要：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-nC6,用嵌套递推的方法,得到了图2-3-nC6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.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.

关 键 词：完美对集 分类 递推式 

分 类 号：O157.5[理学—数学]