• Journal of the Korean Institute of Gas
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• v.16 no.6
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• pp.41-47
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• 2012

There are PFD(Process Flow Diagram) and P&ID(Piping and Instrument Diagram) for designing and managing chemical process efficiently. They provide the operation condition and equipment specifications of chemical process, but they do not provide the reliability of chemical process. Therefore, in this study, Reliability Flow Diagram(RFD) which provide the cycle and time of preventive maintenance has been developed using Directed Graph Analysis methodology. Directed Graph Analysis methodology is capable of assessing the reliability of chemical process. It models chemical process into Directed Graph with nodes and arcs and assesses the reliability of normal operation of chemical process by assessing Directed Graph sequential. In this paper, the chemical process reliability transition according to operation time was assessed. And then, Reliability Flow Diagram has been developed by inserting the result into P&ID. Like PFD and P&ID, Reliability Flow Diagram provide valuable and useful information for the design and management of chemical process.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.8
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• pp.999-1007
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• 1999

이 논문은 재귀원형군 G(2^m , 2^k )를 그래프 이론적 관점에서 고찰하고 정점이 서로소인 사이클과 그래프 invariant에 관한 위상 특성을 제시한다. 재귀원형군은 1 에서 제안된 다중 컴퓨터의 연결망 구조이다. 재귀원형군 {{{{G(2^m , 2^k )가 길이 사이클을 가질 필요 충분 조건을 구하고, 이 조건하에서 G(2^m , 2^k )는 가능한 최대 개수의 정점이 서로소이고 길이가l`인 사이클을 가짐을 보인다. 그리고 정점 및 에지 채색, 최대 클릭, 독립 집합 및 정점 커버에 대한 그래프 invariant를 분석한다.Abstract In this paper, we investigate recursive circulant G(2^m , 2^k ) from the graph theory point of view and present topological properties of G(2^m , 2^k ) concerned with vertex-disjoint cycles and graph invariants. Recursive circulant is an interconnection structure for multicomputer networks proposed in 1 . A necessary and sufficient condition for recursive circulant {{{{G(2^m , 2^k ) to have a cycle of lengthl` is derived. Under the condition, we show that G(2^m , 2^k ) has the maximum possible number of vertex-disjoint cycles of length l`. We analyze graph invariants on vertex and edge coloring, maximum clique, independent set and vertex cover.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.2
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• pp.429-434
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• 2017

In a graph G=(V, E) with n vertices, there is an unique box which is finally laid on each vertex. Thus each vertex and box is both numbered from 1 to n and the box i should be laid on the vertex i. But, the box ${\pi}$(i) is initially located on the vertex i according to a permutation ${\pi}$. In each step, the robot can walk along an edge of G and can carry at most one box at a time. Also when arriving at a vertex, the robot can swap the box placed there with the box it is carrying. The problem is to minimize the total step so that every vertex has its own box, that is, the shuffled boxes are sorted. In this paper, we shall find an upper bound of the minimum number of steps and show that the movement of the robot is found in $O(n^2)$ time when G is a cycle.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1123-1135
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• 1996

In this paper, we introduce some properties of Steinhaus graphs of order n, and prove that the size of some special type of induced cycles in Steinhaus graphs of order n is bounded by $\left\lfloor \frac{n+3}{2} \right\rfloor$.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.279-301
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• 2017

An L(3, 2, 1)-labeling for the graph G = (V, E) is an assignment f of a label to each vertices of G such that ${\mid}f(u)-f({\upsilon}){\mid}{\geq}4-k$ when $dist(u,{\upsilon})=k{\leq}3$. The L(3, 2, 1)-labeling number, denoted by ${\lambda}_{3,2,1}(G)$, for G is the smallest number N such that there is an L(3, 2, 1)-labeling for G with span N. In this paper, we compute the L(3, 2, 1)-labeling number ${\lambda}_{3,2,1}(G)$ when G is a cylindrical grid, which is the cartesian product $P_m{\Box}C_n$ of the path and the cycle, when $m{\geq}4$ and $n{\geq}138$. Especially when n is a multiple of 4, or m = 4 and n is a multiple of 6, then we have ${\lambda}_{3,2,1}(G)=11$. Otherwise ${\lambda}_{3,2,1}(G)=12$.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 1999.05a
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• pp.179-184
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• 1999

A Timing Diagram is almost used to represent the various signals such as an address bus, a data bus, and the control signals during design and analysis of a digital system. But if so, its representation is somewhat complicated and also it is difficult to analyze the operation of the system. In this paper, we proposed the representation method of timing diagrams with the EMFG(Extended Mark Flow Graph). In the EMFG representation of the system operation, the logical states due to the various signals of the system is graphically represented. Therefore the proposal method allows that it is easy to design as well as analyze the system. As examples applied, we represented the memory read cycle of $\mu$PD70320 CPU and the read cycle of MCM60256A memory with the EMFG.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2013.10a
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• pp.773-775
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• 2013

In this paper, we consider the problem for finding a vertex sequence of the directed cycle graph from the individual neighborhood information on a reconfigurable mesh(in short, RMESH). This problem can be solved in linear time using a sequential algorithm. However, it is difficult to develop a sublinear time parallel algorithm for the problem because of its sequential nature. All kinds of polygons can be represented by directed cycles, hence a solution of the problem may be used to solving problems in which a polygon should be constructed from the adjacency information for each vertex. In this paper, we present a constant time $n{\times}n^2$ RMESH algorithm for the problem with n vertices.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.287-302
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• 2008

The vertex set of a digraph D is denoted by V (D). A c-partite tournament is an orientation of a complete c-partite graph. A digraph D is called cycle complementary if there exist two vertex disjoint cycles $C_1$ and $C_2$ such that V(D) = $V(C_1)\;{\cup}\;V(C_2)$, and a multipartite tournament D is called weakly cycle complementary if there exist two vertex disjoint cycles $C_1$ and $C_2$ such that $V(C_1)\;{\cup}\;V(C_2)$ contains vertices of all partite sets of D. The problem of complementary cycles in 2-connected tournaments was completely solved by Reid [4] in 1985 and Z. Song [5] in 1993. They proved that every 2-connected tournament T on at least 8 vertices has complementary cycles of length t and ${\mid}V(T)\mid$ - t for all $3\;{\leq}\;t\;{\leq}\;{\mid}V(T)\mid/2$. Recently, Volkmann [8] proved that each regular multipartite tournament D of order ${\mid}V(D)\mid\;\geq\;8$ is cycle complementary. In this article, we analyze multipartite tournaments that are weakly cycle complementary. Especially, we will characterize all 3-connected c-partite tournaments with $c\;\geq\;3$ that are weakly cycle complementary.

• Magazine of the Korean Society of Agricultural Engineers
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• v.17 no.3
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• pp.3885-3893
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• 1975

This work was intended to study the cutting graph and vibratory phenomina of a newly developed mower which may be suitable for mowing agricultural product having large and hard stems like corn and sugar beet. The system consists of cutter-bar having Curvilinear-translation motion, which attached to drag-crank mechanism. The motion of equation developed for experimental vibratory system which equipped with the cutter-bar system was established and the parameters defining the system's vibratory motion were experimentally determined. The optimum balancing weight for the cutter-bar am vibratory characteristics of the cutter-bar for various counterweight were analyzed to provide the design and operational conditions. The results of the study are summarized as follows; (1) The cutting graph by the new cutter-bar system depends upon the magnitude of ratio of forward travel(Vm) to crank speed (R$\omega$); The cutting pitch for Vm/R$\omega$ 1 (whole cycle cutting) and Vm/R$\omega$=2/$\pi$ (a half cycle cutting) are 2$\pi$ Vm and 4R, respectively. (2) The experimental vibratory system had been proved to function adequately so that it can be used in determining the required counterweight to minimize the vibratory motion of cutter-bar. (3) Experimentally determined counterweight to give the least vibratory motion was a little greater than the theoretically determined one. With the optimum counterweight it was possible to reduce up to about 87% of the amplitude without counterweight, which may be considered to be within safe operational region. (4) To avoid the actual operation of the cutter-bar at resonance which occured in low frequency ratio, it was considered that the rotational speed of the crank for a specific design of mower should be determined separately in connection with the desired cutting graph.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.607-618
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• 2015

An L(2; 1)-labeling of a graph G is a function f from the vertex set V (G) to the set of all non-negative integers such that ${\mid}f(u)-f(v){\mid}{\geq}2$ if d(u, v) = 1 and ${\mid}f(u)-f(v){\mid}{\geq}1$ if d(u, v) = 2. The ${\lambda}$-number of G, denoted ${\lambda}(G)$, is the smallest number k such that G admits an L(2, 1)-labeling with $k=\max\{f(u){\mid}u{\in}V(G)\}$. In this paper, we consider the square of a cycle and provide exact value for its ${\lambda}$-number. In addition, we also completely determine its edge span.