Bounds on the Size of the Minimum Dominating Sets of Some Cylindrical Grid Graphs. (7th April 2014)

• Record Type: Journal Article
• Authors: Nandi, Mrinal; Parui, Subrata; Adhikari, Avishek
• Other Names: Kang Liying Academic Editor.
• Is Part Of: International journal of combinatorics. Volume 2014(2014)
• Publication Date: 2014-04-07
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Periodicals; Electronic journals; 511.605
• DOI: 10.1155/2014/348359
• Languages: English
• ISSNs: 1687-9163

Abstract

Abstract : Letγ P m □ C n denote the domination number of the cylindrical grid graph formed by the Cartesian product of the graphsP m, the path of length m, m ≥ 2, and the graphC n, the cycle of length n, n ≥ 3 . In this paper we propose methods to find the domination numbers of graphs of the formP m □ C n withn ≥ 3 andm = 5 and propose tight bounds on domination numbers of the graphsP 6 □ C n, n ≥ 3 . Moreover, we provide rough bounds on domination numbers of the graphsP m □ C n, n ≥ 3 andm ≥ 7 . We also point out how domination numbers and minimum dominating sets are useful for wireless sensor networks.