Table of Contents
International Journal of Combinatorics
Volume 2013 (2013), Article ID 756179, 6 pages
http://dx.doi.org/10.1155/2013/756179
Research Article

On the Line Graph for Zero-Divisors of

Math. Department, Faculty of Science, The University of Jordan, Amman 11942, Jordan

Received 31 August 2013; Accepted 29 November 2013

Academic Editor: Jun-Ming Xu

Copyright © 2013 Ghada AlAfifi and Emad Abu Osba. 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 be a completely regular Hausdorff space and let be the ring of all continuous real valued functions defined on . In this paper, the line graph for the zero-divisor graph of is studied. It is shown that this graph is connected with diameter less than or equal to 3 and girth 3. It is shown that this graph is always triangulated and hypertriangulated. It is characterized when the graph is complemented. It is proved that the radius of this graph is 2 if and only if has isolated points; otherwise, the radius is 3. Bounds for the dominating number and clique number are also found in terms of the density number of .