| n棱柱的完美匹配计数及其k-共振性 |
| |
| 引用本文： | 杨瑞,刘成立,武楠楠. n棱柱的完美匹配计数及其k-共振性[J]. 山东大学学报(理学版), 2022, 57(11): 37-41. DOI: 10.6040/j.issn.1671-9352.0.2020.518 |
| |
| 作者姓名： | 杨瑞 刘成立 武楠楠 |
| |
| 作者单位： | 河南理工大学数学与信息科学学院, 河南 焦作 454003 |
| |
| 基金项目： | 国家自然科学基金资助项目(11801148,11626089);河南理工大学博士基金项目(B2014-060) |
| |
| 摘 要： | 当n≥3时,笛卡尔积图Cn×P2是一个多面体图,也称为n棱柱,其中Cn为n长圈,P2为2长路。令G是一个n棱柱的平面嵌入图,k是正整数,若对任意的正整数i(0≤i≤k),从图G中任意删除掉i个两两不交的偶面所得到的图有完美匹配,则称图G是k-共振的。首先得到n棱柱完美匹配数的计算公式;然后对n棱柱的共振性进行讨论,得到了n棱柱是1-共振、2-共振的和k-共振的(k≥3)。
|
| 关 键 词： | 完美匹配 笛卡尔积图 n棱柱 k-共振 |
The number of perfect matchings and k-resonance in n-prism |
| |
| YANG Rui,LIU Cheng-li,WU Nan-nan. The number of perfect matchings and k-resonance in n-prism[J]. Journal of Shandong University, 2022, 57(11): 37-41. DOI: 10.6040/j.issn.1671-9352.0.2020.518 |
| |
| Authors: | YANG Rui LIU Cheng-li WU Nan-nan |
| |
| Affiliation: | School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, Henan, China |
| |
| Abstract: | For n≥3, the cartesian product Cn×P2 is a polyhedral graph, the n-prism, where Cn is a n-cycle and P2 is a 2-path. Let G be a plane embedded graph of n-prism and k be a positive integer, the graph G is k-resonant, if the graph obtained by deleting any i pairwise disjoint even faces from the graph G has a perfect matching for any positive integer i(0≤i≤k). The formula of the number of perfect matchings in n-prism is obtained. Then the resonance of n-prism is discussed, its 1-resonance, 2-resonance and k-resonance are obtained(k≥3). |
| |
| Keywords: | perfect matching cartesian product graph n-prism k-resonant |
|
| 点击此处可从《山东大学学报(理学版)》浏览原始摘要信息 |
|
点击此处可从《山东大学学报(理学版)》下载全文 |
|
