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The domination numbers of cylindrical grid graphs |
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| Authors: | Mrinal Nandi |
| Affiliation: | a Department of Statistics, West Bengal State University, Barasat, North 24-Parganas, India b IMBIC, AH 317, Salt Lake City, Calcutta 700091, India c Department of Pure Mathematics, University of Calcutta, 35 Ballygunge Circular Road, Calcutta 700019, India |
| Abstract: | Let γ(Pm □ Cn) denote the domination number of the cylindrical grid graph formed by the Cartesian product of the graphs Pm, the path of length m, m ? 2 and the graph Cn, the cycle of length n, n ? 3. In this paper, methods to find the domination numbers of graphs of the form Pm □ Cn with n ? 3 and m = 2, 3 and 4 are proposed. Moreover, bounds on domination numbers of the graphs P5 □ Cn, n ? 3 are found. The methods that are used to prove that results readily lead to algorithms for finding minimum dominating sets of the above mentioned graphs. |
| Keywords: | Minimum dominating set Grid graph Cycle Path and Cartesian product of graphs |
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