Table of Contents
International Journal of Combinatorics
Volume 2014, Article ID 348359, 13 pages
Research Article

Bounds on the Size of the Minimum Dominating Sets of Some Cylindrical Grid Graphs

1Department of Statistics, West Bengal State University, Barasat, North 24 Parganas 700126, India
2IMBIC, AH 317, Salt Lake City, Calcutta 700091, India
3Department of Pure Mathematics, University of Calcutta, 35 Ballygunge Circular Road, Calcutta 700019, India

Received 30 August 2013; Accepted 23 January 2014; Published 7 April 2014

Academic Editor: Liying Kang

Copyright © 2014 Mrinal Nandi 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.


Let denote the domination number of the cylindrical grid graph formed by the Cartesian product of the graphs , the path of length m, and the graph , the cycle of length n, . In this paper we propose methods to find the domination numbers of graphs of the form with and and propose tight bounds on domination numbers of the graphs , . Moreover, we provide rough bounds on domination numbers of the graphs , and . We also point out how domination numbers and minimum dominating sets are useful for wireless sensor networks.