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Maximum Degree Vertex Domatic Set Algorithm for Domatic Number Problem
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 Title & Authors
Maximum Degree Vertex Domatic Set Algorithm for Domatic Number Problem
Lee, Sang-Un;
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In the absence of a polynomial time algorithm capable of obtaining the exact solutions to it, the domatic number problem (DNP) of dominating set (DS) has been regarded as NP-complete. This paper suggests polynomial-time complexity algorithm about DNP. In this paper, I select a vertex of the maximum degree as an element of a dominating set , compute from a simplified graph of , and verify that is indeed a dominating set through . When applied to 15 various graphs, the proposed algorithm has succeeded in bringing about exact solutions with polynomial-time complexity O(kn). Therefore, the proposed domatic number algorithm shows that the domatic number problem is in fact a P-problem.
Dominating set;Connected DS;Independent DS;Degree;Domatic number;
 Cited by
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