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Title: Total Graphs Associated to a Commutative Ring,
Authors: 4. Khalida Nazzal
Keywords: : total graph, commutative ring, graphs associated to rings.
Issue Date: 30-Jan-2016
Publisher: Palestine Journal of Mathematics, Vol. 5(Special Issue: 1) (2016) , 108–126
Citation: Palestine Journal of Mathematics, Vol. 5(Special Issue: 1) (2016) , 108–126
Series/Report no.: Vol. 5(Special Issue: 1);108–126
Abstract: Let R be a commutative ring with nonzero unity. Let Z(R) be the set of all zerodivisors of R. The total graph of R, denoted by T (Γ(R)), is the simple graph with vertex set R and two distinct vertices x and y are adjacent if their sum x + y ∈ Z(R). Several authors presented various generalizations for T (Γ(R)). This article surveys research conducted on T (Γ(R)) and its generalizations. A historical review of literature is given. Further properties of T (Γ(R)) are also studied. Many open problems are presented for further research.
Description: Main Article
Appears in Collections:Applied science faculty

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