Some properties of the intersection graph for finite commutative principal ideal rings
type: Item
instance of: scholarly article
title: Some properties of the intersection graph for finite commutative principal ideal rings
zbMATH Open document ID: 1302.05079
DOI: 10.1155/2014/952371
author: Emad Abu Osba
author: S. Al-Addasi
author: O. A. AbuGhneim
published in: International Journal of Combinatorics
publication date: 2014-11-17T00:00:00Z
review text: Summary: Let \(R\) be a commutative finite principal ideal ring with unity, and let \(G(R)\) be the simple graph consisting of nontrivial proper ideals of \(R\) as vertices such that two vertices \(I\) and \(J\) are adjacent if they have nonzero intersection. In this paper we continue the work done by Abu Osba. We calculate the radius, eccentricity, domination number, independence number, geodetic number, and the hull number for this graph. We also determine when \(G(R)\) is chordal. Finally, we study some properties of the complement graph of \(G(R)\).
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 6370097
zbMATH Keywords: radius, eccentricity
zbMATH Keywords: domination number
zbMATH Keywords: independence number
zbMATH Keywords: geodetic number
zbMATH Keywords: hull number
Wikidata QID: Q59043584
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/952371
OpenAlex ID: W2167441971
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description: scientific article; zbMATH DE number 6370097