Commutative rings introduce a class of identifiable graphs

Document Type : Research Paper


Department of Mathematics, Jundi-Shapur University of Technology Dezful, Iran



Let $R$ be a commutative ring with identity, and $ \mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ \mathrm{A}(R)^{*}=\mathrm{A}(R)\setminus\lbrace 0\rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, we characterize all positive integers $n$ for which $AG(\mathbb{Z}_n)$ is identifiable.


Main Subjects

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Articles in Press, Corrected Proof
Available Online from 21 February 2024
  • Receive Date: 10 June 2023
  • Revise Date: 28 January 2024
  • Accept Date: 05 February 2024
  • Published Online: 21 February 2024