一类柱面与Mobius带的匹配多项式  

Matching Polynomials of a Class of Cylinders and Mobius Strip

作　　者：马海成[1] 攸晓杰 MA Haicheng;YOU Xiaojie(School of Mathematics and Statistics,Qinghai Nationalities University,Xining 810007,China)

机构地区：[1]青海民族大学数学与统计学院,西宁810007

出　　处：《西南师范大学学报（自然科学版）》2023年第6期35-42,共8页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11561056,11661066);青海省自然科学基金项目(2022-ZJ-924)。

摘　　要：给两条n个点的路,其顶点从左向右分别标记为1,2,…,n和1′,2′,…,n′.将这两条路上的点i和i′(i=1,2,…,n)分别用一条边连接,得到的图记为L_(n,n),称为梯子.将图L_(n,n)的顶点1和n,1′和n′分别用一条边连接得到的图记为Z_(n,n),称为柱面.将图L_(n,n)的顶点1和n′,1′和n分别用一条边连接得到的图记为M_(n,n),称为Mobius带.即L_(n,n)=Pn×P2,Z_(n,n)=Cn×P2分别表示梯子与柱面图.本文利用递推关系和生成函数的方法分别给出了L_(n,n),M_(n,n)和Z_(n,n)的匹配多项式及完美匹配数目的计算公式.Given two paths with n vertices,their vertices are marked as 1,2,…,n and 1′,2′,…,n′from left to right respectively.The ladder L _(n,n) is obtained by connecting the vertices i and i′on these two paths with one edge for i=1,2,…,n,respectively.The cylinder Z _(n,n) is obtained by connecting the vertices 1 and n,and the vertices 1′and n′with one edge on the ladder L _(n,n),respectively.The M bius strip M _(n,n) is obtained by connecting the the vertices 1 and n′,and the vertices 1′and n with one edge respectively on the ladder L _(n,n) That is,L _(n,n)=P n×P 2,Z _(n,n)=C n×P 2.In this paper,the matching polynomials of ladders,cylinder and M bius strip are calculated by using recursive relationships and generation functions.In addition,the number of perfect matching on these graphs are also calculated.

关 键 词：柱面 Mobius带 匹配多项式 完美匹配数 

分 类 号：O157.5[理学—数学]