广义齿轮图的PI指数  

PI Index of Generalized Gear Graph

作　　者：弓文慧 邵燕灵[1] GONG Wenhui;SHAO Yanling(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2024年第3期296-300,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金项目(61774137);山西省回国留学人员科研项目(2022-149);山西省自然科学基金项目(20210302124212)。

摘　　要：设G是简单连通图,e=uv是G中连接点u和点v的一条边,图G的PI指数定义为PI(G)=[neu(e|G)+nev(e|G)]。一个顶点到一条边的距离就是该点与该边的两个端点之间的最小距离。广义齿轮图是通过在圆锥图的圈上的每对相邻顶点之间添加一个顶点而得到的图,其具有优美的对称性。记广义齿轮图C*的PI指数为PI(C*),本文根据广义齿轮图的性质,得到了一种计算与一条边的两个端点距离相等的边的方法,并将其边进行分类,利用此方法找到对PI(C*)没有贡献的边,从而计算出广义齿轮图的PI指数,为研究一些特殊图的PI指数问题提供了线索。Let G be a simple connected graph,e=uv is an edge of the connecting u and v in G,the PI index is defined as PI(G)=∑e=uv∈E(G)[neu(e|G)+nev(e|G)].The distance from a vertex to an edge is taken as the minimum distance between the given point and the two endpoints of that edge.The generalized gear graph is a graph obtained from the conical graph with a vertex added between each pair adjacent verti-ces of the cycles,which has a graceful symmetry.Let PI(C*)be the PI index of generalized gear graph C*.In this paper,the symmetry of generalized gear graph was used to obtain a method to calculate the number of edges that is equidistant from two ends of an edge and classifies its edges.By using this method,we found the edges that did not contribute to PI(C*),and then estimated the PI index of the gen-eralized gear graph,which provided a clue for the study of the PI index of some special graphs.

关 键 词：PI指数 广义齿轮图 偶圈 对称性 

分 类 号：O157.5[理学—数学]