Finite commutative rings with higher genus unit graphs

被引：17

作者：

Su, Huadong ^{[1
,2
]}

Noguchi, Kenta ^{[3
]}

Zhou, Yiqiang ^{[1
]}

机构：

[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[2] Guangxi Teachers Educ Univ, Sch Math & Sci, Nanning 530023, Guangxi, Peoples R China

[3] Keio Univ, Dept Math, Kohoku Ku, Yokohama, Kanagawa 2238522, Japan

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2015年 / 14卷 / 01期

基金：

加拿大自然科学与工程研究理事会; 中国国家自然科学基金;

关键词：

Unit graph; complete graph; complete bipartite graph; genus; finite commutative ring; ZERO-DIVISOR GRAPHS; PLANAR;

D O I：

10.1142/S0219498815500024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R be a ring with identity. The unit graph of R, denoted by G(R), is a simple graph with vertex set R, and where two distinct vertices x and y are adjacent if and only if x + y is a unit in R. The genus of a simple graph G is the smallest nonnegative integer g such that G can be embedded into an orientable surface S-g. In this paper, we determine all isomorphism classes of finite commutative rings whose unit graphs have genus at most three.

引用

页数：14

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