Bounds for the Genus of Generalized Total Graph of a Commutative Ring

• 来源期刊: 代数集刊（英文版）
• 关键词: commutative ring ideal total graph of a ring genus of a graph
• 年，卷（期）: 2019,（3）
• 页码范围: 519-528
• 页数: 10页
• 语种: 英文
• DOI: 10.1142/S1005386719000385

摘要

Let R be a commutative ring with non-zero identity and I its proper ideal.The total graph of R with respect to I,denoted by T(ΓI(R)),is the undirected graph with all elements of R as vertices,and where distinct vertices x and y are adjacent if and only if x + y ∈ S(I) ={a ∈ R:ra ∈ I for some r ∈ R\I}.In this paper,some bounds for the genus of T(ΓI(R)) are obtained.We improve and generalize some results for the total graphs of commutative rings.In addition,we obtain an isomorphism relation between two ideal based total graphs.