TITLE:
The Independence-Separation Problem on the 3-D Rook’s Graph
AUTHORS:
Paul A. Burchett
KEYWORDS:
Chess, Independence-Separation Number, Independence Number, p-Dimensional Grid-Line Graphs, p-Dimensional Rook’s Graph
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.6 No.3,
July
14,
2016
ABSTRACT: 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 rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where ,it is found that when n is odd and , . Conjecture and discussion are added.