图的1-因子数目的递推求法  

Recursive method for the number of 1-factors in graphs

作　　者：唐保祥[1] 任韩[2] TANG Baoxiang;REN Han(School of Mathematics and Statistics,Tianshui Normal University,Tianshui 741001,Gansu Province,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：《浙江大学学报（理学版）》2019年第6期670-675,共6页Journal of Zhejiang University（Science Edition）

基　　金：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。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.

关 键 词：1-因子 线性递推式 特征方程 通解 

分 类 号：O157.5[理学—数学]