Generalized Cayley graphs associated to commutative rings

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• 作者：Mojgan Afkhami^a ; ^{mojgan.afkhami@yahoo.com} ; Kazem Khashyarmanesh^b ; ^{khashyar@ipm.ir} ; Khosro Nafar^b ; ^{khosronafar@yahoo.com}
• 关键词：05C10 ; 13A99
• 刊名：Linear Algebra and its Applications
• 出版年：2012
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：1 August, 2012
• 卷：437
• 期：3
• 页码：1040-1049
• 文件大小：281 K

摘要

Let R be a commutative ring with identity element. For a natural number n, we associate a simple graph, denoted by , with as the vertex set and two distinct vertices X and Y in being adjacent if and only if there exists an lower triangular matrix A over R whose entries on the main diagonal are non-zero and such that or , where, for a matrix B, is the matrix transpose of B. When we consider the ring R as a semigroup with respect to multiplication, then is the usual undirected Cayley graph (over a semigroup). Hence is a generalization of Cayley graph. In this paper we study some basic properties of . We also determine all isomorphic classes of finite commutative rings whose generalized Cayley graph has genus at most three.