中文摘要：

基于图的Gutman指标提出图的顶点Gutman指标.在此基础上,研究了双星树的顶点Gutman指标以及定阶数双星树族的Gutman指标的最值和排序问题,并给出了相应的极值点和极图.

英文摘要：

Based on the Gutman index of graphs, the vertex Gutman index is proposed. On this basis, the extreme values and rankings of the vertex Gutman index of double star trees and the Gutman index of the family of the double star trees with a fixed order are studied, and the corresponding extreme vetices and extreme graphs are given.