On a k-Annihilating Ideal Hypergraph of Local Rings
Keywords:
local ring, k-annihilating ideal hypergraph, Wiener indexAbstract
The concept of a $k$-annihilating ideal hypergraph of a finite commutative ring is very broad, so one of its structures has been discussed, where $R$ is a local ring. In this paper, we present the structure of a $k$-annihilating ideal hypergraph of a local ring and determine the order and size of a $k$-annihilating ideal hypergraph of $\mathcal{AG}_{k}(R)$. We also find and count the degree of every nontrivial ideal of a local ring containing in vertex set $\mathcal{A}(R,k)$, of a hypergraph $\mathcal{AG}_{k}(R)$. Furthermore, we determine the diameter and the center of $\mathcal{A}(R,k)$ that equals 1 or 2. Finally, we compute the Wiener index of a k-annihilating ideal hypergraph of $R$.
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