花束图的Gutman指数
The Gutman Index of Bouquets of Circles
苗红丽 1梅银珍1
作者信息
- 1. 中北大学数学学院,山西太原 030051
- 折叠
摘要
圈Cl,Cm和Cn的单顶点并集同胚于3个自环组成的花束图B3.从图不变量可以刻画复杂网络拓扑性质的角度出发,利用分类讨论的方法,首先讨论了 B3上的顶点Gutman指数;其次,给出了在各个分圈以及B3上的顶点Gutman指数的最大值和最小值;最后,对B3的结果进行推广,得出Bn(n ≥ 4)上的顶点Gutman指数的公式.结果表明,分圈上的顶点Gutman指数的最大值在距离中心的最远处得到,花束图上的顶点Gutman指数的最大值总是在中心处得到,并且最小值都是在最靠近中心的一些顶点处得到.
Abstract
The single-vertex union of Cm,Cn and Cl is homeomorphic to the bouquets of circles B3 consisting of 3 self-loops.In the paper,from the perspective of using graph invariants to describe the topological property of complex networks quantitatively,we firstly use the method of classified discussion and present the vertex Gutman index on B3.Secondly,we study the maximum and minimum of vertex Gutman index on each partition circle and B3,respectively.Finally,we obtain the formula of vertex Gutman index on Bn(n ≥ 4)by generalizing the result of B3.The results show that the maximum of the vertex Gutman index on the split circle is obtained at the farthest distance from the center,the maximum of the vertex Gutman index on the bouquets of circles is always obtained at the center,and the minimum are all obtained at some vertices closest to the center.
关键词
花束图/Gutman指数/最大值/最小值Key words
bouquets of circles/Gutman index/maximum/minimum引用本文复制引用
基金项目
山西省回国留学人员科研项目(22-149)
国家自然科学基金项目(61774137)
山西省自然科学基金项目(20210302124212)
出版年
2024
NETL
NSTL
万方数据