交换环Zn上的零除数图的Gutman指数
The Gutman Index of the Zero-divisor Graph on the Commutative Ring Zn
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
交换环上的零除数图是一个无向的简单连通图,其顶点集为环上的零因子的集合.基于度与距离的Gut-man指数,本文主要采用分类讨论的方法,首先对环上的零除数图进行顶点划分,其次对零除数图的诱导子图上的度与距离及相互之间的连接关系进行讨论,从而刻画出了某些情况下的零除数图的Gutman指数.
Abstract
A zero-divisor graph over a commutative ring is an undirected simple connected graph,whose vertex set is the set of zero factors over the ring.Based on the Gutman index of degree and distance,the method of classification discussion is mainly adopted in this paper.Firstly,the vertex of the zero-divisor graph on the ring is divided.Secondly,the degree and distance on the induced sub-graphs of the zero-divisor graph and the connection relationship between them are discussed.Thus the Gutman index of the zero-di-visor graph in some cases is described.
关键词
Gutman指数/交换环/零除数图/诱导子图Key words
Gutman index/commutative ring/zero-divisor graph/induced subgraph引用本文复制引用
基金项目
国家自然科学基金(61774137)
山西省回国留学人员科研项目(2022-149)
山西省自然科学基金(20210302124212)
出版年
2024
国家科技期刊平台
NSTL
万方数据