Table of Contents
ISRN Discrete Mathematics
Volume 2014 (2014), Article ID 896270, 7 pages
http://dx.doi.org/10.1155/2014/896270
Research Article

The Graph of Equivalence Classes of Zero Divisors

Department of Mathematics, University of Pune, Pune 411007, India

Received 13 December 2013; Accepted 5 February 2014; Published 8 May 2014

Academic Editors: G. Isaak, H.-J. Kreowski, and J. A. Rodriguez Velazquez

Copyright © 2014 Vinayak Joshi 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

We introduce a graph of equivalence classes of zero divisors of a meet semilattice with 0. The set of vertices of are the equivalence classes of nonzero zero divisors of and two vertices and are adjacent if and only if . It is proved that is connected and either it contains a cycle of length 3 or . It is known that two Boolean lattices and have isomorphic zero divisor graphs if and only if . This result is extended to the class of SSC meet semilattices. Finally, we show that Beck's Conjecture is true for .