• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.181-192
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• 2003

We count the numbers of independent dominating sets of rooted labeled trees, ordinary labeled trees, and recursive trees, respectively.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.17-25
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• 2021

A set D ⊆ V (G) is an independent transversal dominating set of G if D is a dominating set and also intersects every maximum independent set in G. The minimum cardinality of such a set is equal to the transversal domination number, denoted by ��it(G). This paper is devoted to the computation of the independent transversal domination number of some complementary prism.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1077-1097
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• 2017

In this research article, we introduce certain concepts, including domination, total domination, strong domination, weak domination, edge domination and total edge domination in m-polar fuzzy graphs. We describe these concepts by several examples. We investigate some related properties of certain dominations in m-polar fuzzy graphs. We also present a decision making method based on domination in m-polar fuzzy graphs.

• Journal of the Korea Society of Computer and Information
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• v.18 no.9
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• pp.121-129
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• 2013

This paper proposes a linear-time algorithm that has been designed to obtain an accurate solution for Dominating Set (DS) problem, which is known to be NP-complete due to the deficiency of polynomial-time algorithms that successfully derive an accurate solution to it. The proposed algorithm does so by repeatedly assigning vertex v with maximum degree ${\Delta}(G)$among vertices adjacent to the vertex v with minimum degree ${\delta}(G)$ to Minimum Independent DS (MIDS) as its element and removing all the incident edges until no edges remain in the graph. This algorithm finally transforms MIDS into Minimum DS (MDS) and again into Minimum Connected DS (MCDS) so as to obtain the accurate solution to all DS-related problems. When applied to ten different graphs, it has successfully obtained accurate solutions with linear time complexity O(n). It has therefore proven that Dominating Set problem is rather a P-problem.

• Journal of the Korea Society of Computer and Information
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• v.20 no.2
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• pp.63-70
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• 2015

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 $v_i$ of the maximum degree ${\Delta}(G)$ as an element of a dominating set $D_i,i=1,2,{\cdots},k$, compute $D_{i+1}$ from a simplified graph of $V_{i+1}=V_i{\backslash}D_i$, and verify that $D_i$ is indeed a dominating set through $V{\backslash}D_i=N_G(D_i)$. 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.