k-tuple domination for some chessboard graphs

Abstract

In this paper we consider k-tuple domination on the n×n bishop’s, rook’s, and queen’s graphs. For the n×n bishop’s graph, we solve the k-tuple domination number when k=n-1 and when k=n-3. For the n×n rook’s graph we find the k-tuple domination number for all n >1 and all j, with 0 ≤ n/2-1 ≤ j and k=2n-2-2j. Finally, for the n×n queen’s graph, a lower bound for the k-tuple domination number is found for k=3n-3.