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The authors present a systematic approach to selecting cluster heads in regular mesh topologies based on the idea of k-Domination in graphs. Given a graph, G=(V,E), a subset D of V is said to be a 1-dominating set if every node v in V is either in D or is adjacent to a node in D. A subset D is said to be a k-dominating set if every node v, not in D, is connected to a node in D via a path of length less than or equal to k.
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