两类树图的加权Szeged指标的界  

Bounds of weighted Szeged index of two kinds of tree graphs

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

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《山东大学学报(理学版)》2025年第2期34-40,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11961040)。

摘　　要：给定一个连通图G,图G的加权Szeged指标的定义为S_(w)(G)=∑/uv=e∈E(G) (d_(G)(u)+d_(G)(v))n^(G)_(U)(e)n^(G)_(U)(e),其中,d_(G)(u)表示图G的顶点u的度,n^(G)_(U)(e)表示图G中距离顶点u比顶点v近的顶点个数。首先给出了一些图变换,然后利用这些图变换得到了繁星的加权Szeged指标的上界、下界以及给定直径的树图的加权Szeged指标的上界,并刻画了相应的极值图。Given a graph G,the weighted Szeged index of a graph G,denoted by S_(w)(G)=∑/uv=e∈E(G) (d_(G)(u)+d_(G)(v))n^(G)_(U)(e)n^(G)_(U)(e)where d_(G)(u)is the degree of u in G.For edge uv=e E E(G),n_(u)(e)represents the number of vertices closer to vertex u than vertex v in graph G.Some graph transformations are given,by using these graph transformations,the upper bound and lower bound of weighted Szeged index of blossomed stars and the upper bound of weighted Szeged index of trees with given diameters are obtained,and the corresponding extreme value graphs are characterized.

关 键 词：加权Szeged指标 繁星 树 

分 类 号：O157.5[理学—数学]