Taiwanese Journal of Mathematics

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

T. Tamizh Chelvam and S. Nithya

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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 $\Gamma_\mathcal{I}(N)$.

Article information

Source
Taiwanese J. Math., Volume 17, Number 5 (2013), 1613-1625.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706228

Digital Object Identifier
doi:10.11650/tjm.17.2013.2739

Mathematical Reviews number (MathSciNet)
MR3106033

Zentralblatt MATH identifier
1301.16053

Subjects
Primary: 16Y30: Near-rings [See also 12K05] 05C69: Dominating sets, independent sets, cliques

Keywords
zero-divisor graph 3-prime ideal domination spectrum of 3-prime ideals

Citation

Tamizh Chelvam, T.; Nithya, S. DOMINATION IN THE ZERO-DIVISOR GRAPH OF AN IDEAL OF A NEAR-RING. Taiwanese J. Math. 17 (2013), no. 5, 1613--1625. doi:10.11650/tjm.17.2013.2739. https://projecteuclid.org/euclid.twjm/1499706228


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