亚苯基链关于k-独立集数的极链  

Extremal phenylene chains on k-independent sets

作　　者：谢明芳 潘蕴静 XIE Mingfang;PAN Yunjing(Department of Mathematics and Physics,Fujian Jiangxia University,Fuzhou 350108,China;Chengyi College,Jimei University,Xiamen 361021,China)

机构地区：[1]福建江夏学院数理教研部,福建福州350002 [2]集美大学诚毅学院,福建厦门361021

出　　处：《厦门大学学报（自然科学版）》2024年第6期1089-1094,共6页Journal of Xiamen University：Natural Science

摘　　要：[目的]针对含有n个六边形的亚苯基链关于k-独立集数的极链问题进行了研究.[方法]通过亚苯基链的Y-多项式的递推式及归纳法,给出线性链L_(n),亚苯基链PH_(n)以及螺旋链H_(n)的Y-多项式之间的偏序关系,来确定亚苯基链关于k-独立集数的极链.[结果]亚苯基链关于k-独立集数的极大链为线性链L_(n),极小链为螺旋链H_(n).[结论]本文为了确定亚苯基链关于k-独立集数的极链,着力去寻找亚苯基链的Y-多项式的递推式,及确定亚苯基链Y-多项式之间的偏序关系,这将对后续研究如Merrifield-Simmons指标等提供帮助.[Objective] In this paper,we study the problem of extremal phenylene chains with n hexagons on k-independent sets.[Methods] We show the partial order relationship among the linear chain,phenylene chain and helical chain by the recursion relation of Y-polynomial of phenylene chain and the inducion method.Then we use the partial order relationship of phenylene chains to determine extremal phenylene chains on k-independent sets.[Results] We show that the maximal chain on k-independent sets is a linear chain,and the minimal chain is a helical chain.In addition,we also determine the recursion relation of Y-polynomial of phenylene chain.[Conclusion] To determine extremal phenylene chains with n hexagons on k-independent sets,we try to find the recursion relation of Y-polynomial of phenylene chains.Hopefully,our study may contribute to subsequent studies such as Merrifield-Simmons index,and determine the partial order relationship of Y-polynomial of phenylene chains.

关 键 词：亚苯基链 k-独立集数 Y-多项式 

分 类 号：O157.6[理学—数学]