عنوان البحث(Papers / Research Title)
Domination in Isosceles Triangular Chessboard
الناشر \ المحرر \ الكاتب (Author / Editor / Publisher)
احمد عبد علي عمران المعموري
Citation Information
احمد,عبد,علي,عمران,المعموري ,Domination in Isosceles Triangular Chessboard , Time 19/12/2016 18:53:41 : كلية التربية للعلوم الصرفة
وصف الابستركت (Abstract)
Domination in Isosceles Triangular Chessboard
الوصف الكامل (Full Abstract)
One of the classical chessboard problems is placing minimum number of one type of pieces such that all unoccupied positions are under attack. This problem is called the domination number problem of P. This number is denoted by ?(P) and we denote the number of different methods for placing P pieces to obtain the domination number of P by S(?(P)). Also we are interested in the domination number of two different types of pieces by fixing a number of one type P of pieces and determine the domination number ( ? , ) of another type ?of pieces. Finally we compute (( ?, )). In n square chessboard (see [4], [5] and [6]) ? is studied for rook "R", bishop "B" and king "K" .They proved that ?(R) = , ?(B) = and ?(K) =
. In [3], JoeMaio and William proved that ?(R) = min {m, } for mxn Toroidal chessboards. A saw-toothed chessboard, or STC for short, is a kind of chessboard whose boundary forms two staircases from left down to right without any hole inside it. In [2] Hon-Chan Chena, Ting-Yem Hob, determined the minimum number of rooks that can dominate all squares of the STC. Dietrich and Harborth [1] studied the triangular triangle board, i.e. the board in the shape of a triangle with triangular cells. They defined the chess pieces in particular the rook which attacks in straight lines from a side of the triangle to a side of the triangle, forming rhombuses, the bishop 1 which attacks from vertex to side, side to vertex etc. in straight lines, forming diamonds, and for the bishop 2: the triangular triangle board can be 2- coloured, whose cells are sharing an edge of different color, and the bishop 2 moves as bishop 1, but attacks only cells of the same color.
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