Bounds on the Size of the Minimum Dominating Sets of Some Cylindrical Grid Graphs. (7th April 2014) - Nandi, Mrinal; Parui, Subrata; Adhikari, Avishek
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.