Classification of Genus Three Zero-Divisor Graphs

被引：0

作者：

Asir, Thangaraj ^{[1
]}

Mano, Karuppiah ^{[2
]}

Alsuraiheed, Turki ^{[3
]}

机构：

[1] Pondicherry Univ, Dept Math, Pondicherry 605014, India

[2] Fatima Coll, Dept Math, Madurai 625018, India

[3] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 12期

关键词：

local ring; zero-divisor graph; graph embedding; RINGS;

D O I：

10.3390/sym15122167

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we consider the problem of classifying commutative rings according to the genus number of its associating zero-divisor graphs. The zero-divisor graph of R, where R is a commutative ring with nonzero identity, denoted by Gamma(R), is the undirected graph whose vertices are the nonzero zero-divisors of R, and the distinct vertices x and y are adjacent if and only if xy=0. Here, we classify the local rings with genus three zero-divisor graphs.

引用

页数：15

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