Maximum Degree Vertex Domatic Set Algorithm for Domatic Number Problem

- Journal title : Journal of the Korea Society of Computer and Information
- Volume 20, Issue 2, 2015, pp.63-70
- Publisher : Korean Society of Computer Information
- DOI : 10.9708/jksci.2015.20.2.063

Title & Authors

Maximum Degree Vertex Domatic Set Algorithm for Domatic Number Problem

Lee, Sang-Un;

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 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.

Keywords

Dominating set;Connected DS;Independent DS;Degree;Domatic number;

Language

Korean

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