• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.193-204
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• 2022

A subset S of V(G), where G is a simple undirected graph, is a hop dominating set if for each v ∈ V(G)＼S, there exists w ∈ S such that d_G(v, w) = 2 and it is a locating-hop set if N_G(v, 2) ∩ S ≠ N_G(v, 2) ∩ S for any two distinct vertices u, v ∈ V(G)＼S. A set S ⊆ V(G) is a locating-hop dominating set if it is both a locating-hop and a hop dominating set of G. The minimum cardinality of a locating-hop dominating set of G, denoted by 𝛄_lh(G), is called the locating-hop domination number of G. In this paper, we investigate some properties of this newly defined parameter. In particular, we characterize the locating-hop dominating sets in graphs under some binary operations.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.741-752
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• 2023

A new variant of vertex edge domination, namely semi total vertex edge domination has been introduced in the present paper. A subset S of the vertex set V of a graph G is said to be a semi total vertex edge dominating set(stved - set), if it is a vertex edge dominating set of G and each vertex in S is within a distance two of another vertex in S. An stved-set of G having minimum cardinality is said to be an γ_stve(G)- set and its cardinality is denoted by γ_stve(G). Bounds for γ_stve(G) - set have been given in terms of various graph theoretic parameters and graphs attaining the bounds have been characterized. In particular, bounds for trees have been obtained and extremal trees have been characterized.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1193-1207
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• 2023

In this paper, we introduce an iP₂ extension of a star graph S_n for n ≥ 2 and 1 ≤ i ≤ n - 1. Certain general properties satisfied by order, size, domination (or Roman) numbers γ (or γ_R) of an iP₂ extended star graph are studied. Finally, we study how the parameters such as chromatic number and harmonious chromatic number are affected when an iP₂ extension process acts on the star graphs.

• Proceedings of the Korean Institute of Industrial Safety Conference
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• 1998.11a
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• pp.231-237
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• 1998

현대산업에서는 눈부신 기술의 발달로 모든 시스템이 대형화, 복잡화되고 있다. 이들 시스템의 고장은 사회적으로 커다란 문제를 야기할 수 있으며, 이에 이들 시스템의 신뢰도 계산은 필요하다. 이때 신뢰도계산을 목적으로 Network나 통신망 등의 시스템구조는 비방향성 graph로 아주 쉽게 표현될 수 있다. 지금까지는 시스템의 신뢰도 계산방법중 가장 빠른 것으로는 domination이론을 이용한 것들이 발표되었으나, 모두 방향성 graph(directed graph)에 대한 연구(1∼8)이었다. 이에 본 연구에서는 non direct graph에서 domination성질을 관찰하여보고, 이의 결과를 기초로 하여 효과적인 신뢰도 계산방법과 식을 제시하여 본다. (중략)

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.335-342
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• 1996

Suppose $k$ is a field and $M$ is the set of all $m \times n$ matrices over $k$. If T is a linear operator on $M$ and f is a function defined on $M$, then T preserves f if f(T(A)) = f(A) for all $A \in M$.

• Communications for Statistical Applications and Methods
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• v.20 no.4
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• pp.329-337
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• 2013

Consider a p-variate($p{\geq}3$) normal distribution with mean ${\theta}$ and covariance matrix ${\sum}={\sigma}^2{\mathbf{I}}_p$ for any unknown scalar ${\sigma}^2$. In this paper we improve the James-Stein estimator of ${\theta}$ in cases of shrinking toward some vectors using the Stein variance estimator. It is also shown that this domination does not hold for the positive part versions of these estimators.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.917-933
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• 2017

In this paper, seven equivalent conditions of complete moment convergence and complete integral convergence for negatively orthant dependent (NOD, in short) sequences are shown under two cases: identical distribution and stochastic domination. The results obtained in the paper improve and generalize the corresponding ones of Liang et al. [10]). In addition, an extension of the Baum-Katz complete convergence theorem: six equivalent conditions of complete convergence is established.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.857-863
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• 2013

In this paper, we prove that the total domination number of a $P_6$-free graph of order $n{\geq}3$ and minimum degree at least one which is not the cycle of length 6 is at most $\frac{n+1}{2}$, and the bound is sharp.

• Journal of Internet Computing and Services
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• v.18 no.2
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• pp.113-121
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• 2017

As the industrial structure of the mobile telecommunications market is transforming into the ICT ecosystem centered on smartphones, the regulatory system conforming to the new ICT environment has become the main subject of discussion in key developed countries. The EU segmented the mobile phone service into wholesale and retail. Simultaneously, the EU appraised mobile telecommunication carriers' market domination in segmented markets to continuously improve the scheme to promote competition in the telecommunications market. In Korea, also, there is discussion about adopting the EU scheme to segment the mobile phone market definition more finely and taking measures to appraise the market domination in accordance with object appraisal criteria. As such, this study analyzes whether the current criteria for appraising the wholesale termination rate market domination under the ICT's domestic mobile telecommunication ecosystem is adequate and presents the rational improvement measures reflecting the theoretically suggested evaluation factors.

• ETRI Journal
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• v.15 no.2
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• pp.27-34
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• 1993

Pitman-Intransitive triples of estimators are constructed, based on prior work on equivariant estimators and prior work on shrinkage.