若干哈林图的Balaban指标

The Balaban Index of Several Halin Graphs

摘要: 在树的Balaban指标的研究基础上，本文通过列举4阶到10阶内满足条件的若干哈林图，由其特殊性质入手，给出一种新的哈林图的表达方式，探索哈林图类的Balaban指标的变化规律，总结归纳出哈林图类中不同结构下的最大$J\left(G\right)$ 指标和其最大$J$ 指标下的$SJ\left(G\right)$ 指标的一般公式，并给出若干哈林图Balaban指标的上界。

Abstract: Based on the research on the Balaban index of trees, this paper first enumerates several Halin graphs that meet the specified criteria and have orders ranging from 4 to 10. Starting from their special properties, a new expression method for Halin graphs is proposed. Then, the variation law of the Balaban index for the class of Halin graphs is explored. Finally, the general formulas for the maximum $J\left(G\right)$ index under different structures within the Halin graph class and the $SJ\left(G\right)$ index corresponding to this maximum $J\left(G\right)$ index are summarized and concluded, and the upper bounds of the Balaban index for several Halin graphs are provided.