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| Paper IPM / M / 7809 |
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| Abstract: | |||||||
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Let R be a commutative ring with nonzero identity and
let I be an ideal of R. The zero-divisor graph of R with
respect to I, denoted by ΓI(R), is the graph whose
vertices are the set {x ∈ R\I| xy ∈ I forsome y ∈ R\I} with distinct vertices x and y
adjacent if and only if xy ∈ I. In the case I=0,
Γ0(R), denoted by Γ(R), is the zero-divisor graph
which has well known results in the literature. In this article we
explore the relationship between ΓI(R) ≅ ΓJ(S) and Γ(R/I) ≅ Γ(S/J). We also discuss when ΓI(R) is bipartite. Finally we give some
results on the subgraphs and the parameters of ΓI(R).
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