交换环Z_(n)上的零除数图的Gutman指数  

The Gutman Index of the Zero-divisor Graph on the Commutative Ring Z_(n)

作　　者：苗红丽 梅银珍[1] MIAO Hongli;MEI Yinzhen(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《山西大学学报（自然科学版）》2024年第2期295-301,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：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)。

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Gutman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。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 subgraphs of the zero-divisor graph and the connection relationship between them are discussed.Thus the Gutman index of the zero-divisor graph in some cases is described.

关 键 词：Gutman指数 交换环 零除数图 诱导子图 

分 类 号：O157.5[理学—数学]