The k-Power Domination Number in Some Self-Similar Graphs
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The k-power domination problem is a problem in graph theory, which has applications in many areas. However, it is hard to calculate the exact k-power domination number since determining k-power domination number of a generic graph is a NP-complete problem. We determine the exact k-power domination number in two graphs which have the same number of vertices and edges: pseudofractal scale-free web and Sierpiński gasket. The k-power domination number becomes 1 for k>2 in the Sierpiński gasket, while the k-power domination number increases at an exponential rate with regard to the number of vertices in the pseudofractal scale-free web. The scale-free property may account for the difference in the behavior of two graphs.
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