• Title/Summary/Keyword: Graph theory

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H-TREES, RESTRICTIONS OF DOWLING GROUP GEOMETRIES

  • Mphako-Banda, Eunice
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.3
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    • pp.955-962
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    • 2015
  • It has been established that the role played by complete graphs in graph theory is similar to the role Dowling group geometries and Projective geometries play in matroid theory. In this paper, we introduce a notion of H-tree, a class of representable matroids which play a similar role to trees in graph theory. Then we give some properties of H-trees such that when q = 0, then the results reduce to the known properties of trees in graph theory. Finally we give explicit expressions of the characteristic polynomials of H-trees, H-cycles, H-fans and H-wheels.

A Study on the Guidance Signage System of Outpatient in General Hospital using Spatial Configuration Theory - View from G.D.Weisman's Way-finding Influence Factors (공간구조론을 적용한 종합병원 외래부 유도사인 배치 및 평가에 관한 연구 - G.D.Weisman의 길찾기 요소를 중심으로)

  • Kim, Suktae;Paik, Jinkyung
    • Journal of The Korea Institute of Healthcare Architecture
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    • v.21 no.3
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    • pp.25-35
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    • 2015
  • Purpose: Signs that are installed at unnoticeable places or that disconnect before the destination can bring errors of location information delivery. Therefore, this study aims to find out the spatial relation between structure of space and signs in the perspective of visual exposure possibility, operating arrangement and assesment by applying spatial structure theory. Methods: Effectiveness of organization of guidance signs was evaluated after the four way-finding factors(Plan Configuration, Sign System, Perceptual Access, Architectural Difference) that G.D.Weisman suggested were interpreted by spatial structure theory(J-Graph analysis, Space Syntax, Visual Graph Analysis) under the premise that it is closely related to the structure of space. Results: 1) Because the south corridor that connects each department of outpatient division is located in the hierarchy center of the space, and walking density is expected to be high, guidance signs need to be organized at the place with high integration value. 2) The depth to the destination space can be estimated through J-Graph analysis. The depth means a switch of direction, and the guidance signs are needed according to the number. 3) According to visibility graph analysis, visual exposure can be different in the same hierarchy unit space according to the shape of the flat surface. Based on these data, location adjustment of signs is possible, and the improvement effect can be estimated quantitatively. Implications: Spatial structure theory can be utilized to design and evaluate sign systems, and it helps to clearly understand the improvement effect. It is desirable to specify design and estimation of sign systems in the order of J-Graph analysis${\rightarrow}$Space Syntax Theory${\rightarrow}$visibility graph analysis.

Mobile robot indoor map making using fuzzy numbers and graph theory

  • Kim, Wan-Joo;Ko, Joong-Hyup;Chung, Myung-Jin
    • 제어로봇시스템학회:학술대회논문집
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    • 1993.10b
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    • pp.491-495
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    • 1993
  • In this paper, we present a methodology to model an indoor environment of a mobile robot using fuzzy numbers and to make a global map of the robot environment using graph theory. We describe any geometric primitive of robot environment as a parameter vector in parameter space and represent the ill-known values of the prameterized geometric primitive by means of fuzzy numbers restricted to appropriate membership functions. Also we describe the spatial relations between geometric prinitives using graph theory for local maps. For making the global map of the mobile robot environment, the correspondence problem between local maps is solved using a fuzzy similarity measure and a Bipartite graph matching technique.

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Optimal Layout for Irrigation Pipeline Networks using Graph Theory (Graph 이론을 이용한 농업용 관수로망의 최적배치)

  • Im, Sang-Jun;Park, Seung-Woo;Cho, Jae-Pil
    • Journal of Korean Society of Rural Planning
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    • v.6 no.2 s.12
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    • pp.12-19
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    • 2000
  • Irrigation pipeline networks consist mainly of buried pipes and are therefore relatively free from topographic constraints. Installation of irrigation pipeline systems is increasing since the systems have several advantages compared to open channel systems. To achieve economic design of pipeline networks, the layout should meet several conditions such as shortest path, maximum flow, and least cost. Graph theory is mathematical tool which enable to find out optimum layout for complicated network systems. In this study, applicability of graph theory to figure out optimum layout of irrigation pipeline networks was evaluated.

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On Matroids

  • Kim, Yuon Sik
    • The Mathematical Education
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    • v.13 no.3
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    • pp.22-32
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    • 1975
  • Matroid와 transversal theory에 관한 연구가 활발하게 진행되고 있다. 이 논문은 circuit matroid가 transversal이 되기 위한 필요 충분 조건을 지적하고 이를 증명한 것이다. 곧 어떤 graph의 circuit matroid가 transversal이 되기 위한 필요 충분 조건은 그 graph가 graph $K_4$거나 $C_{k}$ $^{2}$에 homeomorphic인 subgraph를 포함하지 않은 것이다. 증명의 방법으로는 주로 matroid의 cocircuit의 성질을 사용하여 transversal Matroid의 presentation을 적절하게 적용하고 graph의 reduction과 contraction을 이용한다.

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초평면 배열 이론과 4색 문제

  • 이기석;왕문옥;이준호
    • Journal for History of Mathematics
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    • v.15 no.1
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    • pp.147-168
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    • 2002
  • In this paper, we introduce the arrangement of hyperplanes and the graph theory. In particular, we explain how to study the 4-color problem by using characteristic polynomials of the arrangement of hyperplanes. The 4-color problem was appeared in 1852 at first and Appel and Haken proved it by using computer in 1976. The arrangement of hyperplanes induced from a graph is called a graphic arrangement. Graphic arrangement is a subarrangement of Braid arrangement. Thus the chromatic function of a graph is equal to the characteristic polynomial of a graphic arrangement. If we use this result, we can apply the theory of the arrangement of hyperplanes to the study for the chromatic functions.

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Systematics in Fishing Navigation Efficiency Increasing

  • Zhidkov, E.M.;Malyavin, E.N.
    • Journal of the Korean Institute of Navigation
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    • v.22 no.2
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    • pp.81-87
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    • 1998
  • On this paper, the methods of optimization research of the fishing navigation using the graph theory are substantiated on the basis of the proposed probable model of the fishing vessel navigator's activity. The graph theory is concered about the transitionform the top graph to the rib one. And the definition of the additional system elements (quasi elements) necessary to provide the effectiveness during the fishing navigation are also substantiated herein. This approach helps to optimize the structure of any fishing vessel monitoring system.

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Recent developments of constructing adjacency matrix in network analysis

  • Hong, Younghee;Kim, Choongrak
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.5
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    • pp.1107-1116
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    • 2014
  • In this paper, we review recent developments in network analysis using the graph theory, and introduce ongoing research area with relevant theoretical results. In specific, we introduce basic notations in graph, and conditional and marginal approach in constructing the adjacency matrix. Also, we introduce the Marcenko-Pastur law, the Tracy-Widom law, the white Wishart distribution, and the spiked distribution. Finally, we mention the relationship between degrees and eigenvalues for the detection of hubs in a network.

AN OPTIMAL PARALLEL ALGORITHM FOR SOLVING ALL-PAIRS SHORTEST PATHS PROBLEM ON CIRCULAR-ARC GRAPHS

  • SAHA ANITA;PAL MADHUMANGAL;PAL TAPAN K.
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.1-23
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    • 2005
  • The shortest-paths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents an $O(n^2)$ time sequential algorithm and an $O(n^2/p+logn)$ time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, where p and n represent respectively the number of processors and the number of vertices of the circular-arc graph.

A Dependability Modeling of Software Under Memory Faults for Digital System in Nuclear Power Plants

  • Park, Jong-Gyun;Seong, Poong-Hyun
    • Nuclear Engineering and Technology
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    • v.29 no.6
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    • pp.433-443
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    • 1997
  • In this work, an analytic approach to the dependability of software in the operational phase is suggested with special attention to the hardware fault effects on the software behavior : The hardware faults considered are memory faults and the dependability measure in question is the reliability. The model is based on the simple reliability theory and the graph theory which represents the software with graph composed of nodes and arcs. Through proper transformation, the graph can be reduced to a simple two-node graph and the software reliability is derived from this graph. Using this model, we predict the reliability of an application software in the digital system (ILS) in the nuclear power plant and show the sensitivity of the software reliability to the major physical parameters which affect the software failure in the normal operation phase. We also found that the effects of the hardware faults on the software failure should be considered for predicting the software dependability accurately in operation phase, especially for the software which is executed frequently. This modeling method is particularly attractive for the medium size programs such as the microprocessor-based nuclear safety logic program.

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