On a \(k\)-Annihilating Ideal Hypergraph of Local Rings - Essa, Shaymaa S.; Mohammad, Husam Q. (Communications in Mathematics and Applications, 2024)
The concept of a \(k\)-annihilating ideal hypergraph of a finite commutative ring is very broad, and one of its structures has been discussed, where \(R\) is a local ring. In this paper, the structure of a \(k\)-annihilating ideal hypergraph of local rings is presented and the order and size of it are determined. Also, the degree of every nontrivial \(k\)-annihilating ideal of local rings containing in the vertex set \(\mathcal{A}(R,k)\) of a hypergraph \(\mathcal{AG}_{k}(R)\) is found and counted. Furthermore, the diameter of a \(k\)-annihilating ideal hypergraph \(\mathcal{AG}_{k}(R)\) is determined, which equals 1 or 2, as well as the centre of \(\mathcal{AG}_{k}(R)\). Finally, the Wiener index of a \(k\)-annihilating ideal hypergraph \(\mathcal{AG}_{k}(R)\) is computed.
Keywords: Local ring; k-annihilating ideal hypergraph; Wiener index