Maximum Degree Vertex Domatic Set Algorithm for Domatic Number Problem

Title & Authors
Maximum Degree Vertex Domatic Set Algorithm for Domatic Number Problem
Lee, Sang-Un;

Abstract
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 $\small{v_i}$ of the maximum degree $\small{{\Delta}(G)}$ as an element of a dominating set $\small{D_i,i=1,2,{\cdots},k}$, compute $\small{D_{i+1}}$ from a simplified graph of $\small{V_{i+1}=V_i{\backslash}D_i}$, and verify that $\small{D_i}$ is indeed a dominating set through $\small{V{\backslash}D_i=N_G(D_i)}$. 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.
Keywords
Dominating set;Connected DS;Independent DS;Degree;Domatic number;
Language
Korean
Cited by
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