图的覆盖数与分子的凯库勒结构  

Covering Number of Graphs and KekuléStructure of Molecules

作　　者：胡启明 许欢 袁晓彤 HU Qi-ming;XU Huan;YUAN Xiao-tong(Department of Basic Course Teaching,Hefei Preschool Education College,Hefei 230013,China)

机构地区：[1]合肥幼儿师范高等专科学校公共教学部,安徽合肥230013

出　　处：《长春师范大学学报》2022年第4期17-21,共5页Journal of Changchun Normal University

基　　金：合肥幼儿师范高等专科学校科研创新团队“图论科研创新团队”(KCTD202001);合肥幼儿师范高等专科学校2019年度校级立项教科研项目“泛圈图的拓扑指数刻画”(hyzyb2019009);合肥幼儿师范高等专科学校2019年度校级立项教科研项目“图的哈密尔顿性的谱刻画”(hyzzd2019003)。

摘　　要：化学分子图通常是以原子为顶点、以共价键为边的无向图.图中含有完美匹配等价于化学分子的凯库勒结构.本文利用点覆盖数和边覆盖数来证明化学图中凯库勒结构的存在性,讨论因子临界图当点覆盖数和边覆盖数相等或相差1时的顶点数与独立数间的关系,并讨论了顶部梯状图和广义梯形图的点覆盖数和边覆盖数.Chemical molecular graphs can be regarded as undirected graphs with atoms as vertices and covalent bonds as edges.The perfect match in the graph is equivalent to the Kekuléstructures in chemical graphs.In this paper,we first prove the existence of Kekuléstructure in chemical graphs by using the number of point covers and edge covers.Then,we discuss the relationship between the number of vertices and the number of independences in factor critical graphs when the number of vertex covers and the number of edge covers are equal or different by 1.Finally,we discuss the number of point covers and the number of edge covers of top ladder graphs and generalized ladder graphs.

关 键 词：点覆盖数 边覆盖数 凯库勒图 因子临界图 顶部梯状图 广义梯形图 

分 类 号：O157.5[理学—数学]