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.
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页数：15
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