泛圈图关于Wiener指数和hyper-Wiener指数的充分条件  

A Sufficient Condition for Wiener Index and Hyper-Wiener Index of Pancyclic Graph

作　　者：李青 梅培林 胡启明 LI Qing;MEI Peilin;HU Qiming

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 [2]安庆师范大学数理学院,安徽安庆246004

出　　处：《芜湖职业技术学院学报》2023年第3期44-46,50,共4页Journal of Wuhu Institute of Technology

基　　金：2020年度安徽高校自然科学研究重点项目“关于谱与拓扑指数极图的研究”(项目号:KJ2020A0894);2022年度合肥幼儿师范高等专科学校教科研重点项目“图的拓扑指数与哈密尔顿性”(项目号:hykyzd202206)。

摘　　要：泛圈图是指包含所有长度为l(3≤l≤n)的圈的n阶简单连通图。根据满足边条件e(G)的简单连通图G的特性,结合连通图及其补图的Wiener指数和hyper-Wiener指数与边条件e(G)的关联式,得出连通图G要成为泛圈图所需满足的充分条件:W(G)≤n^(2)+5n-30/2,W(G)≥n^(3)-8n^(2)+43n-60/2,WW(G)≤n^(2)+11n-60/2,WW(G)≥n^(4)-8n^(3)+37n^(2)-18n-60/2。Pancyclic graph means a n-order simple connected graph containing all circles with the length of l(3≤l≤n).According to the property of the simple connected graph G meeting the edge condition e(G),in view of the correlation of the Wiener index and hyper-Wiener index of a connected graph and its complementary graph with the edge condition e(G),a sufficient condition for the connected graph G to become a pancyclic graph is concluded as follows:W(G)≤n^(2)+5n-30/2,W(G)≥n^(3)-8n^(2)+43n-60/2,WW(G)≤n^(2)+11n-60/2,WW(G)≥n^(4)-8n^(3)+37n^(2)-18n-60/2.

关 键 词：WIENER指数 hyper-Wiener指数 泛圈图 

分 类 号：O157.5[理学—数学]