n棱柱的完美匹配计数及其k-共振性  

The number of perfect matchings and k-resonance in n-prism

作　　者：杨瑞 刘成立 武楠楠 YANG Rui;LIU Cheng-li;WU Nan-nan(School of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo 454003,Henan,China)

机构地区：[1]河南理工大学数学与信息科学学院,河南焦作454003

出　　处：《山东大学学报（理学版）》2022年第11期37-41,49,共6页Journal of Shandong University(Natural Science)

基　　金：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C_(n)×P_(2)是一个多面体图,也称为n棱柱,其中C_(n)为n长圈,P_(2)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)。For n≥3,the cartesian product C_(n)×P_(2)is a polyhedral graph,the n-prism,where C_(n)is a n-cycle and P_(2)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).

关 键 词：完美匹配 笛卡尔积图 n棱柱 k-共振 

分 类 号：O157.6[理学—数学]