| 唐保祥,任韩.一类3-正则图完美对集的计数[J].,2020,60(4):437-440 |
| 一类3-正则图完美对集的计数 |
| Enumeration of perfect matchings of a type of 3-regular graphs |
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| DOI：10.7511/dllgxb202004013 |
| 中文关键词:完美对集分类递推式 |
| 英文关键词:perfect matchingclassificationrecursive formula |
| 基金项目:国家自然科学基金资助项目(11171114). |
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| 摘要点击次数:420 |
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| 中文摘要: |
| 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． |
| 英文摘要: |
| 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. |
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