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Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 587196, 7 pages
http://dx.doi.org/10.1155/2013/587196
Research Article

Construction of Dominating Sets of Certain Graphs

1Department of Mathematics, Yazd University, Yazd 89195-741, Iran
2Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Malaysia

Received 15 November 2012; Accepted 1 February 2013

Academic Editor: Wai Chee Shiu

Copyright © 2013 Saeid Alikhani and Yee-Hock Peng. 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 simple graph. A set is a dominating set of , if every vertex in is adjacent to at least one vertex in . We denote the family of dominating sets of a graph with cardinality by . In this paper we introduce graphs with specific constructions, which are denoted by . We construct the dominating sets of by dominating sets of graphs , , and . As an example of , we consider . As a consequence, we obtain the recursive formula for the number of dominating sets of .