@article{Essa_Mohammad_2024, title={On a \(k\)-Annihilating Ideal Hypergraph of Local Rings}, volume={15}, url={http://www.rgnpublications.com/journals/index.php/cma/article/view/2378}, DOI={10.26713/cma.v15i1.2378}, abstractNote={<p>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.</p>}, number={1}, journal={Communications in Mathematics and Applications}, author={Essa, Shaymaa S. and Mohammad, Husam Q.}, year={2024}, month={Apr.}, pages={253–263} }