在直径为d的树中具有极小GA2的树

摘要

Tabar等人定义了图的第二类几何-算术指标GA2,同时给出了任意连通图G的可达上下界,并分别刻画了:在有n个顶点的树中Pn具有极大GA2,K1,n-1具有极小GA2.刘颖在有n个顶点的树中确定了具有GA2前五小的图及在具有完美匹配的所有树中具有GA2前四小的图.在此基础上,本文给出直径固定且有n个顶点的树中具有极小GA2的图.%Tabar et al have defined the second geometric-arithmetic index GA2. They gave the upper and lower bounds of all connected graphs and determined the tree Pn with the maximal GA2 ,the tree Ki,n-1 with the minimal GA2 among all the tree with n vertices. Liu gave the graphs with the first fifth smallest GA2 with n vertices and the graphs with the first fourth smallest GA2 with perfect matching. In this paper, we determine the graphs with the minimal GA2 among all the tree with diameter d.