Table of Contents
International Journal of Combinatorics
Volume 2014 (2014), Article ID 952371, 6 pages
http://dx.doi.org/10.1155/2014/952371
Research Article

Some Properties of the Intersection Graph for Finite Commutative Principal Ideal Rings

1Department of Mathematics, The University of Jordan, Amman 11942, Jordan
2Department of Mathematics, Hashemite University, Zarqa 13115, Jordan

Received 28 May 2014; Accepted 10 September 2014; Published 25 September 2014

Academic Editor: Johannes Hendrik Hattingh

Copyright © 2014 Emad Abu Osba et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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).