Bishop Independence
Liam H. Harris
Mathematics and Statistics, University of South Wales, Pontypridd, CF37 1DL, UK.
Stephanie Perkins *
Mathematics and Statistics, University of South Wales, Pontypridd, CF37 1DL, UK.
Paul A. Roach
Mathematics and Statistics, University of South Wales, Pontypridd, CF37 1DL, UK.
Siân K. Jones
Mathematics and Statistics, University of South Wales, Pontypridd, CF37 1DL, UK.
*Author to whom correspondence should be addressed.
Abstract
Bishop Independence concerns determining the maximum number of Bishops that can be placed on a board such that no Bishop can attack any other Bishop. This paper presents the solution to the Bishop Independence problem, determining the Bishop Independence number, for all sizes of boards on the following topologies: the cylinder, the M¨obius strip, the torus, the Klein bottle and the surface of a cube.
Keywords: Graph, Bishop Graph, Independence, Bishop Independence, Chess, Chessboard