The Independence-Separation Problem on the 3-D Rook’s Graph ()
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.
Share and Cite:
Burchett, P. (2016) The Independence-Separation Problem on the 3-D Rook’s Graph.
Open Journal of Discrete Mathematics,
6, 167-173. doi:
10.4236/ojdm.2016.63014.
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