加权Szeged指标的上下界  

On the Upper and Lower Bounds of Weighted Szeged Index

作　　者：胡姣 刘蒙蒙 HU Jiao;LIU Mengmeng(School of Mathematics and Science,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《洛阳理工学院学报（自然科学版）》2022年第4期88-92,共5页Journal of Luoyang Institute of Science and Technology：Natural Science Edition

基　　金：甘肃高等学校创新能力提升项目(2019A-37)

摘　　要：给定一个连通图,图G的加权Szeged指标的定义为wSz(G)=∑_(uv=e∈E(G))(d_(G)(u)+d_(G)(v))n_(u)(e)n_(v)(e)。其中,d_(G)(u)表示图G的顶点u的度,n_(u)(e)表示图G中距离顶点u比顶点v近的顶点个数。首先给出加权Szeged指标的上界,并刻画了达到上界的极值图。再根据加权Szeged指标与其他拓扑指标、直径之间的关系,得到了不同条件下的加权Szeged指标的下界,并刻画了相应的极值图。The weighted Szeged index of the graph G is defined as wSz(G)=∑_(uv=e∈E(G))(d_(G)(u)+d_(G)(v))n_(u)(e)n_(v)(e),where d_(G)(u)is the degree of the vertex u in G;n_(u)(e)represents the number of vertices closer to vertex u than_(v)ertex v in graph G.Firstly,this paper gives the upper bound of weighted Szeged index,and characterizes the extremum graph reaching the upper bound.Secondly,according to the relationship between the weighted Szeged index and other topological indexes and diameters,the lower bounds of the weighted Szeged index under different conditions are obtained,and the corresponding extremum graphs are characterized.

关 键 词：加权Szeged指标 Szeged指标 第一Zagreb指标 

分 类 号：O157.5[理学—数学]