平面二部图的Clar覆盖多项式  

The Clar Covering Polynomials of Plane Bipartite Graphs

作　　者：刘莹 王广富 高新宇 Liu Ying;Wang Guangfu;Gao Xinyu(School of Science,East China Jiaotong University,Nanchang 330013,China;School of Mathematics and Information Scienes,Yantai University,Yantai 264000,China)

机构地区：[1]华东交通大学理学院,江西南昌330013 [2]烟台大学数学与信息科学学院,山东烟台264000

出　　处：《华东交通大学学报》2025年第1期120-126,共7页Journal of East China Jiaotong University

基　　金：国家自然科学基金项目(11861032,11961026);江西省自然科学基金项目(20202BABL201010)。

摘　　要：Clar覆盖多项式是表征分子图共轭体系电子结构的一种方法。通过研究平面二部图的Clar覆盖多项式,可以深入探讨相关分子图的共振理论及其性质。基于平面二部图的Clar覆盖多项式的相关定理,利用生成函数的方法计算平面二部图的Clar覆盖多项式;推导出一类特殊图的Clar覆盖多项式的递推关系,并利用生成函数的方法计算两类Cata型平面二部图的Clar覆盖多项式的显式表达式。根据平面二部图的Clar覆盖多项式,可以了解化学分子的电子结构,预测其化学性质和反应行为,并设计新的分子结构。The Clar covering polynomial of molecular graphs is a method to characterize the electronic structure of conjugated systems.By studying the Clar covering polynomials of plane bipartite graphs,the resonance theo-ry of related molecular graphs and their properties can be thoroughly investigated.Based on the theorem related to Clar covering polynomials of plane bipartite graphs,the method of generating functions is utilized to compute Clar covering polynomials of plane bipartite graphs.Recurrence relationship for Clar covering polynomials of a special class of graphs are derived.In turn,explicit expressions the Clar covering polynomials of two classes of catacondensed plane bipartite graphs are computed using the generating function method.On the Clar covering polynomials of plane bipartite graphs,it is possible to understand the electronic structure of chemical molecules,predict their chemical properties and reaction behavior,and design new molecular structures.

关 键 词：平面二部图 Clar覆盖多项式 递推关系 显式表达式 

分 类 号：O157.5[理学—数学]