Dominance of graphs in Zpn and in Z3n×Z2>m

In this paper we describe the problem of finding minimal domination subsets for graphs of the kind Zpⁿ and Z3ⁿ×Z2^m. We use a simulating annealing algorithm to compute upper bounds of the cardinality of sub-minimal dominating subsets. We demonstrate the effectiveness of the algorithm by comparing the results with a previously studied class of graphs, including the so-called “football pool” graphs and others. We give some new upper bounds for graphs of the kind Zpⁿ, with p≥4.