Some Properties of the Intersection Graph for Finite Commutative Principal Ideal Rings. (25th September 2014)

• Record Type: Journal Article
• Authors: Abu Osba, Emad; Al-Addasi, Salah; Abughneim, Omar
• Other Names: Hattingh Johannes Hendrik Academic Editor.
• Is Part Of: International journal of combinatorics. Volume 2014(2014)
• Publication Date: 2014-09-25
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Periodicals; Electronic journals; 511.605
• DOI: 10.1155/2014/952371
• Languages: English
• ISSNs: 1687-9163

Abstract

Abstract : 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) .