%0 Journal Article
%T The Number of Minimum Roman and Minimum Total Dominating Sets for Some Chessboard Graphs
%A Paul A. Burchett
%J Open Journal of Discrete Mathematics
%P 31-44
%@ 2161-7643
%D 2020
%I Scientific Research Publishing
%R 10.4236/ojdm.2020.101004
%X In this paper, both the roman domination number and the number of minimum roman dominating sets are found for any rectangular rook¡¯s graph. In a similar fashion, the roman domination number and the number of minimum roman dominating sets are found on the square bishop¡¯s graph for odd board sizes. Also found are the number of minimum total dominating sets associated with the light-colored squares when <em>n</em>&nbsp;<span style=\"white-space:nowrap;\">&amp;#8801; 1(mod12)&nbsp;</span> (with<em> n</em>&gt;1), and same for the dark-colored squares when <em style=\"white-space:normal;\">n</em><span style=\"white-space:normal;\">&nbsp;</span>&amp;#8801; 7(mod12) .
%K Total Domination
%K Roman Domination
%K Bishop¡¯s Graph
%K Rook¡¯s Graph
%K Chess
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=97890