棱柱和Mobius梯的Tutte多项式  

Tutte polynomials of prisms and Mobius ladders

作　　者：吕江 赵海兴[2,3] 邓波 LV Jiang;ZHAO Hai-xing;DENG Bo(College of Mathematics and Statistics,Qinghai Normal University,Xining 810016,China;College of Computer,Qinghai Normal University,Xining 810016,China;The State Key Laboratory of Tibetan Intelligent Information Processing and Application,Xining,810016,China)

机构地区：[1]青海师范大学数学与统计学院,青海西宁810016 [2]青海师范大学计算机学院,青海西宁810016 [3]藏语智能信息处理及应用国家重点实验室,青海西宁810016

出　　处：《青海师范大学学报（自然科学版）》2024年第1期46-52,共7页Journal of Qinghai Normal University(Natural Science Edition)

基　　金：青海省自然科学基金项目(2022-ZJ-T02);111引智计划项目(D20035);国家自然科学基金项目(12261073)。

摘　　要：棱柱是圈C_(n)和路P_(2)的笛卡尔积,也可以看作两端连接的梯图.Mobius梯的结构与棱柱相似,可看作扭曲后两端连接的梯图,并且自然地嵌入Mobius带.图的Tutte多项式是一个双变量多项式图不变量,通过对变量赋值或变换可以得到生成树数目、连通生成子图数目、色多项式和可靠多项式等许多图不变量.本文运用Tutte多项式的删除-收缩运算,获得了棱柱和Mobius梯的Tutte多项式.A prism is a cartesian product of the cycle and the path can also be seen as a ladder graph connected at both ends.The structure of a Mobius ladder is similar to that of a prism,and can be seen as a twisted ladder graph connected at both ends,naturally embedded with straps.The Tutte polynomial of a graph is a bivariate polynomial graph invariant.By assigning or transforming variables,many graph invariants can be obtained,such as the number of spanning trees,the number of connected spanning subgraphs,chromatic polynomials,and reliability polynomials.This article uses the deletion-contraction operation of the Tutte polynomial to obtain the Tutte polynomials for prisms and Mobius ladders.

关 键 词：棱柱 Mobius梯 Tutte多项式 

分 类 号：O157.5[理学—数学]