On the Associated Graphs to a Commutative Ring
نویسندگان
چکیده
Let R be a commutative ring with non-zero identity. For an arbitrary multiplicatively closed subset S of R, we associate a simple graph denoted by ΓS(R) with all elements of R as vertices, and two distinct vertices x, y ∈ R are adjacent if and only if x + y ∈ S. Two well-known graphs of this type are the total graph and the unit graph. In this paper, we study some basic properties of ΓS(R). Moreover, we will improve and generalize some results for the total and the unit graphs.
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