• Korea and Global Affairs
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• v.1 no.2
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• pp.129-148
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• 2017

The political system of Xi Jinping which was launched in 2013, faced many difficulties both domestically and internationally. Xi Jinping must integrate and stabilize society through political reforms, such as sustained economic growth and Resolved corruption. In addition, he should seek new relations with the United States on the denuclearization of the Korean peninsula. Therefore, this study analyzed political leadership of Chinese political leaders including Xi Jinping using Max Weber 's political domination type. From the first generation political leaders to the fourth generation political leaders in China, the types of political domination of the first and second generation political leaders tend to be charismatic rather than legitimate domination. But the third generation political leaders tend to have a tendency of traditional domination rather than legitimate domination, and the fourth generation political leaders have a tendency to dominate more than traditional domination. On the other hand, the type of political domination of Xi Jinping shows traditional domination and legitimate domination tendency in the process of political growth and emergence, but shows tendency of charismatic domination after domination of political power.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.181-188
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• 2004

Recently, Zhang et al. [6] obtained some lower bounds of the signed domination number of a graph. In this paper, we obtain some new lower bounds of the signed domination number of a graph which are sharper than those of them.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.205-219
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• 2002

We deride formulas for the expected values $\mu$(n) of the independent domination numbers of a random planted plane tree and a random trivalent tree with n vertices, respectively, and we determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.921-931
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• 2004

We derive a formula for the expected value $\mu$(n) of the independent domination number of a random directed rooted tree with n labeled vertices and determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.1115-1121
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• 2007

In this paper, we consider cooperative games arising from integer total domination problem on graphs. We introduce two games, rigid integer total domination game and its relaxed game, and focus on their cores. We give characterizations of the cores and the relationship between them.

• Journal of the Korean Society of Safety
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• v.11 no.1
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• pp.16-26
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• 1996

In a series of original papers, [1-17] efficient methods and algorithms have been presented, for the exact solution of many reliability problems represented by binary networks. A starting point of these methods was the concept of domination, firstly introduced in ,elation with reliability problems in [2]. It's application to directed networks resulted in the development of a topological formula for the classical problem of the two terminal reliability. This result was extended later to the all-terminal and the k-terminal reliability problems. All papers mentioned above use a path oriented representation for the network topology. In practical applications, however, it is common and often advantageous to work with cut sets. This article considers the Domination theory for reliability problem of a network. Some topological formula are derived and the power and the application of this formula are shown through the alternative proof of topological formula of A. Satyanarayana [2].

• East Asian mathematical journal
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• v.23 no.1
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• pp.1-8
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• 2007

In this paper, we introduce the concept of strong and weak domination in fuzzy graphs, and provide some examples to explain various notions introduced. Also some properties discussed.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.359-366
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• 2014

A three-valued function f defined on the vertices of a digraph D = (V, A), $f:V{\rightarrow}\{-1,0,+1\}$ is a minus total dominating function(MTDF) if $f(N^-(v)){\geq}1$ for each vertex $v{\in}V$. The minus total domination number of a digraph D equals the minimum weight of an MTDF of D. In this paper, we discuss some properties of the minus total domination number and obtain a few lower bounds of the minus total domination number on a digraph D.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.631-638
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• 2018

Chellai et al. [3] gave an upper bound on the [1, 2]-domination number of tree and posed an open question "how to classify trees satisfying the sharp bound?". Yang and Wu [5] gave a partial solution for tree of order n with ${\ell}$-leaves such that every non-leaf vertex has degree at least 4. In this paper, we give a new upper bound on the [1, 2]-domination number of tree which extends the result of Yang and Wu. In addition, we design a polynomial time algorithm for solving the open question. By using this algorithm, we give a characterization on the [1, 2]-domination number for trees of order n with ${\ell}$ leaves satisfying $n-{\ell}$. Thereby, the open question posed by Chellai et al. is solved.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.505-519
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• 2023

Let G = (V, E) be a graph. A subset S of V is called a dominating set of G if every vertex not in S is adjacent to some vertex in S. The domination number γ(G) of G is the minimum cardinality taken over all dominating sets of G. A dominating set S is called a connected dominating set if the subgraph induced by S is connected. The minimum cardinality taken over all connected dominating sets of G is called the connected domination number of G, and is denoted by γ_c(G). In this paper, we investigate the Nordhaus-Gaddum type results for the connected domination number and its derived graphs like line graph, subdivision graph, power graph, block graph and total graph, and characterize the extremal graphs.