基于字典序乘积下广义和连通度指标的上下界  

Sharp Bounds on General Sum-Connectivity Index Based on Lexicographic Product

作　　者：李志豪[1] 朱焱 LI Zhihao;ZHU Yan(School of Mathematics,East China University of Science and Technology,Shanghai 200237,China)

机构地区：[1]华东理工大学数学学院,上海200237

出　　处：《华东理工大学学报（自然科学版）》2022年第3期405-410,共6页Journal of East China University of Science and Technology

基　　金：国家自然科学基金(11671135)。

摘　　要：对于图G,令E(G),d_(G)(v)分别表示G的边集和顶点v的度。对于边e=uv,定义广义和连通度指标χ_(α)(e)=(d_(G)(u)+d_(G)(v))^(α),其中α为任意实数。在对两个简单的连通图G和H做乘积之前,先对其中一个图H进行S,R,Q,T4种运算,运算后的图记为F(H)(其中F∈{S,R,Q,T}),再对图G和F(H)做字典序乘积,给出了基于字典序乘积下图的广义和连通度的指标上下界,并且这些界都是最好的。Give a graph G,let E(G)and d_(G)(v)respectively.For an edge e=uv,the general sum-connectivity index is χ_(α)(e)=(d_(G)(u)+d_(G)(v))^(α),in which α is any real number.Before taking the product of two simple connected graphs G and H,we first perform four operations of S,R,Q,Ton the graph H,denoted as F(H),in which F∈{S,R,Q,T},then take the lexicographical product of graphs G and F(H)lexicographic product are given,and these bounds are sharp.

关 键 词：广义和连通度指标 字典序乘积 图的4种运算 F-和 

分 类 号：O157[理学—数学]