加权Szeged指标的上下界

On the Upper and Lower Bounds of Weighted Szeged Index

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.