引用本文:唐保祥, 任韩.2类图完美匹配计数公式的嵌套递推求法[J].西南师范大学学报(自然科学版),2019,44(8):23~27
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2类图完美匹配计数公式的嵌套递推求法
唐保祥, 任韩1,2
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
摘要:
把图2-nD8和2-nD6的完美匹配按饱和某个顶点的完美匹配进行分类,求出每一类完美匹配数目的递推关系式,再利用这些递推式之间的相互关系,得到这两类图的完美匹配数目的递推关系式,最后从递推式中解出这两类图的完美匹配数目的计算公式.
关键词:  完美匹配  线性递推式  特征方程  通解
DOI:10.13718/j.cnki.xsxb.2019.08.005
分类号:O157.5
基金项目:国家自然科学基金项目(11171114).
Two Types of Nested Recursive Methods for Finding Counting Formulas of Perfect Matching Number
TANG Bao-xiang, REN Han1,2
1. School of Mathematics and Statistics, Tianshui Normal University, Tianshui Gansu 741001, China;2. Department of Mathematics, East China Normal University, Shanghai 200062, China
Abstract:
The perfect matching of graphs 2-nD8 and 2-nD6 has been classified according to the perfect matching of a certain vertex of saturation, and the recursive relation of each kind of perfect matching number been obtained. Then the interrelationship between these recursive formulas has been used to eliminate those that are not needed. The recursive relation has been used to obtain the recursive relation of the perfect matching number of the two kinds of graphs. Finally, the formula for calculating the perfect matching number of the two graphs has been solved from the recursive formula.
Key words:  perfect matching  linear recurrence relation  characteristic equation  general solution
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