### DOMINATION IN THE ZERO-DIVISOR GRAPH OF AN IDEAL OF A NEAR-RING

#### Abstract

Let $N$ be a near-ring. In this paper, we associate a graph corresponding to the $3$-prime radical $\mathcal{I}$ of $N$, denoted by $\Gamma_\mathcal{I}(N)$. Further we obtain certain topological properties of $Spec(N)$, the spectrum of $3$-prime ideals of $N$ and graph theoretic properties of $\Gamma_\mathcal{I}(N)$. Using these properties, we discuss dominating sets and connected dominating sets of $\Gamma_\mathcal{I}(N)$.

#### Keywords

Zero-divisor graph, 3-Prime ideal, Domination, Spectrum of 3-prime ideals

| ISSN 1027-5487(Print), ISSN 2224-6851 (Online) |