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

LetNbe a near-ring. In this paper, we associate a graph corresponding to the 3-prime radical ℐ ofN, denoted by Γℐ(N). Further we obtain certain topological properties ofSpec(N), the spectrum of 3-prime ideals ofNand graph theoretic properties of Γℐ(N). Using these properties, we discuss dominating s...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 17; no. 5; pp. 1613 - 1625
Main Authors Chelvam, T. Tamizh, Nithya, S.
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.10.2013
Subjects
Mathematical rings
Mathematical sets
Topological spaces
Topological theorems
Topology
Vertices
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Summary:LetNbe a near-ring. In this paper, we associate a graph corresponding to the 3-prime radical ℐ ofN, denoted by Γℐ(N). Further we obtain certain topological properties ofSpec(N), the spectrum of 3-prime ideals ofNand graph theoretic properties of Γℐ(N). Using these properties, we discuss dominating sets and connected dominating sets of Γℐ(N). 2010Mathematics Subject Classification: Primary 16Y30; Secondary 05C69. Key words and phrases: Zero-divisor graph, 3-Prime ideal, Domination, Spectrum of 3-prime ideals.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.17.2013.2739