• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.871-882
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• 2012

For a connected graph G of order $n$, an ordered set $S=\{u_1,u_2,{\cdots},u_k\}$ of vertices in G is a linear edge geodetic set of G if for each edge $e=xy$ in G, there exists an index $i$, $1{\leq}i$ < $k$ such that e lie on a $u_i-u_{i+1}$ geodesic in G, and a linear edge geodetic set of minimum cardinality is the linear edge geodetic number $leg(G)$ of G. A graph G is called a linear edge geodetic graph if it has a linear edge geodetic set. The linear edge geodetic numbers of certain standard graphs are obtained. Let $g_l(G)$ and $eg(G)$ denote the linear geodetic number and the edge geodetic number, respectively of a graph G. For positive integers $r$, $d$ and $k{\geq}2$ with $r$ < $d{\leq}2r$, there exists a connected linear edge geodetic graph with rad $G=r$, diam $G=d$, and $g_l(G)=leg(G)=k$. It is shown that for each pair $a$, $b$ of integers with $3{\leq}a{\leq}b$, there is a connected linear edge geodetic graph G with $eg(G)=a$ and $leg(G)=b$.

• Journal of the Korean Society of Safety
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• v.13 no.2
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• pp.136-144
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• 1998

FTA is the most commonly used method among quantitative safety assessment. In case that the observing system become larger, a lot of terms should be calculated to accomplish FTA through complicated process. Many methods have been tried to reduce time, one of tries is How to calculate the reliability using graph theory after changing W to graph. This paper suggests an algorithm that can calculate more rapidly reliability and outset of system expressed by non-linear graph as like as FTA or CCA.

• Proceedings of the Korean Institute of Industrial Safety Conference
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• 1997.05a
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• pp.95-109
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• 1997

보통 시스템은 신뢰도 계산을 위하여 graph나 fault tree(FT)등으로 그 시스템의 신뢰도 특성을 표현하게 된다. 전산망이나 교통망등은 보통 하나의 부품이 graph의 한선에 1:1로 대응하는 linear graph로 표현되나 화학공장이나 원자력 발전소의 신뢰성 분석을 위하여 쓰이는 FT는 보통 하나의 부품 또는 사건이 여러 곳에서 나타나는 non linear graph이다. (중략)

• Journal for History of Mathematics
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• v.23 no.4
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• pp.83-100
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• 2010

This paper is to raise several questions in teaching the Graph and Linear Transformation complied with the Mathematics Amended Curriculum announced in 2006 Aug. and then to formulate a plan accordingly. For this, we'll take a good look at the prior studies on the Graph and Linear Transformation after the announcement of the 7th School Curriculum along with the changes in their contents through the process of curriculum. Then we'll check over learning factors of the Graph and Linear Transformation in all 27 kinds of the authorized textbooks - 'Mathematics I', 'Applications of Mathematics', and 'Geometry and Vectors' - and 27 kinds of exercise books issued on 2009. By this, we put measures which improve understanding and apply correctly to the Graph and Linear Transformation in the Mathematics Amended Curriculum to high school teachers.

• Proceedings of the Korean Institute of Industrial Safety Conference
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• 1997.05a
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• pp.111-116
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• 1997

공학적 신뢰도 문제에서 부품의 신뢰도나 가동도가 주어진 후 시스템의 신뢰도 평가를 위한 수치적 계산이 자주 요구된다. 이때 주어진 system은 graph나 fault tree등으로 신뢰도 특성을 표현하게 된다. 보통 network이나 교통망 등은 graph로 표현되며 부품과 graph의 선이 1 : 1로 대응되는 linear graph 이다. 이러한 그래프에 대한 신뢰도를 분석하는 방법 중에 여러 가지가 있으나 본 연구에서는 domination이론을 이용하여 신뢰도를 계산한다. (중략)

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.573-580
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• 2012

A (1, ${\lambda}$)-embedded graph is a graph that can be embedded on a surface with Euler characteristic ${\lambda}$ so that each edge is crossed by at most one other edge. A graph $G$ is called ${\alpha}$-linear if there exists an integral constant ${\beta}$ such that $e(G^{\prime}){\leq}{\alpha}v(G^{\prime})+{\beta}$ for each $G^{\prime}{\subseteq}G$. In this paper, it is shown that every (1, ${\lambda}$)-embedded graph $G$ is 4-linear for all possible ${\lambda}$, and is acyclicly edge-($3{\Delta}(G)+70$)-choosable for ${\lambda}$ = 1, 2.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.87-95
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• 2019

The homothety classes of lattices in a two dimensional vector space over a nonarchimedean local field form a regular tree ${\mathcal{T}}$ of degree q + 1 on which the projective linear group acts naturally where q is the order of the residue field. We show that for any finite regular combinatorial graph of even degree q + 1, there exists a torsion free discrete subgroup ${\Gamma}$ of the projective linear group such that ${\mathcal{T}}/{\Gamma}$ is isomorphic to the graph.

• Korean Journal of Mathematics
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• v.9 no.1
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• pp.53-60
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• 2001

We study the properties of positivity of matrices and construct useful positive matrices. As an application, we consider a directed graph with matrices such that all the associated matrices related to the positive linear functional are positive.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.6 s.336
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• pp.49-58
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• 2005

In this paper, we propose an optimal ILP scheduling algorithm for multiprocessor design on LDFG(Linear Data-Flow Graph) that can be represented by homogeneous synchronous data-flow. The proposed computation in this paper does not contain data-dependent, all scheduling decisions for such algorithms can be taken at compile time, only fully static overlapped schedules are considered. It means that all linear have the same schedule and the same processor assignment. In this paper, the resource-constrained problem is addressed, for the LDFG optimization for multiprocessor design problem formulating ILP solution available to provide optimal solution. The results show that the scheduling method is able to find good quality schedules in reasonable time.

• Communications for Statistical Applications and Methods
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• v.15 no.1
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• pp.27-41
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• 2008

A graphical method of checking the adequacy of a generalized linear model is proposed. The graph helps to assess the assumption that the link function of mean can be expressed as a linear combination of explanatory variables in the generalized linear model. For the graph the boosting technique is applied to estimate nonparametrically the relationship between the link function of the mean and the explanatory variables, though any other nonparametric regression methods can be applied. Through simulation studies with normal and binary data, the effectiveness of the graph is demonstrated. And we list some limitations and technical details of the graph.