%0 Journal Article
%T The Independence-Separation Problem on the 3-D RookĄ¯s Graph
%A Paul A. Burchett
%J Open Journal of Discrete Mathematics
%P 167-173
%@ 2161-7643
%D 2016
%I Scientific Research Publishing
%R 10.4236/ojdm.2016.63014
%X Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rookĄ¯s graph. A lower bound of k, for <img src=\"Edit_938a31c8-c6d2-4ad7-943d-891b08918bf7.bmp\" alt=\"\" />, is found for the independence-separation number on the d-dimensional rookĄ¯s graph, denoted by <img src=\"Edit_1e3aec20-7a5e-4493-913e-ca52d9e77820.bmp\" alt=\"\" />. For the case where <img src=\"Edit_4fc5718c-52ef-4ea2-b939-a22aaddc74a7.bmp\" alt=\"\" />,&nbsp;it is found that when n is odd and <img src=\"Edit_1385e4b0-51f6-42a3-b6d5-ebbc4874e69c.bmp\" alt=\"\" />, <img src=\"Edit_3a55afb0-e9cb-4c04-a024-97d8acb429a9.bmp\" alt=\"\" />. Conjecture and discussion are added.
%K Chess
%K Independence-Separation Number
%K Independence Number
%K p-Dimensional Grid-Line Graphs
%K p-Dimensional RookĄ¯s Graph
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=68335