TY - JOUR
AU - Essa, Shaymaa S.
AU - Mohammad, Husam Q.
PY - 2024/04/24
Y2 - 2024/11/07
TI - On a \(k\)-Annihilating Ideal Hypergraph of Local Rings
JF - Communications in Mathematics and Applications
JA - Comm. Math. Appl.
VL - 15
IS - 1
SE - Research Article
DO - 10.26713/cma.v15i1.2378
UR - http://www.rgnpublications.com/journals/index.php/cma/article/view/2378
SP - 253 - 263
AB - <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>
ER -