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| 图的1-因子数目的递推求法 | |
| 引用本文： | 唐保祥,任韩.图的1-因子数目的递推求法[J].浙江大学学报(理学版),2019,46(6):670-675. |
| 作者姓名： | 唐保祥 任韩 |
| 作者单位： | 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 |
| 基金项目： | 国家自然科学基金资助项目(11171114). |
| 摘 要： | 首先对图的1-因子进行分类，求出每一类1-因子数目的递推关系式；然后对各类1-因子数目的递推式进行求和，得到一组有相互联系的递推关系式；利用递推式之间的相互关系，消去不需要的，得到图的1-因子数目的递推关系式；最后求出此递推式的公式解。 |
| 关 键 词： | 1-因子 线性递推式 特征方程 通解 |
| 收稿时间： | 2018-08-17 |
Recursive method for the number of 1-factors in graphs |
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| TANG Baoxiang,REN Han.Recursive method for the number of 1-factors in graphs[J].Journal of Zhejiang University(Sciences Edition),2019,46(6):670-675. | |
| Authors: | TANG Baoxiang REN Han |
| Institution: | 1.School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, Gansu Province,China 2.Department of Mathematics, East China Normal University, Shanghai 200062 , China |
| Abstract: | First, we classify the 1-factor of the graph, find the recurrence relation of the number of 1-factors of each class, and then， sum the recursive numbers of 1-factor numbers of each class to obtain a set of interconnected recursive relations. Then, with the relationship between these recursive formulas, we eliminate the unnecessary recurrence relations, obtain the recurrence relation of the 1-factor number of this graph, finally derive the formula solution of this recurrence formula. |
| Keywords: | 1-factor linear recurrence relation characteristic equation general solution |
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