Commutative rings introduce a class of identifiable graphs

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 ۰\rbrace and two distinct vertices I and J are adjacent if and only if IJ=۰ . In this paper, we characterize all positive integers n for which AG(\mathbb{Z}_n) is identifiable.

کلیدواژه ها:

Annihilating-ideal graph ، Identifying code ، Identifiable Graph