• Title/Summary/Keyword: Graph theory

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Genesis and development of Schur rings, as a bridge of group and algebraic graph theory (Schur환론의 발생과 발전, 군론과 그래프론에서의 역할)

  • Choi Eun-Mi
    • Journal for History of Mathematics
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    • v.19 no.2
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    • pp.125-140
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    • 2006
  • In 1933, I. Schur introduced a Schur ring in connection with permutation group and regular subgroup. After then, it was studied mostly for purely group theoretical purposes. In 1970s, Klin and Poschel initiated its usage in the investigation of graphs, especially for Cayley and circulant graphs. Nowadays it is known that Schur ring is one of the best way to enumerate Cayley graphs. In this paper we study the origin of Schur ring back to 1933 and keep trace its evolution to graph theory and combinatorics.

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ON THE SCHULTZ POLYNOMIAL AND HOSOYA POLYNOMIAL OF CIRCUMCORONENE SERIES OF BENZENOID

  • Farahani, Mohammad Reza
    • Journal of applied mathematics & informatics
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    • v.31 no.5_6
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    • pp.595-608
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    • 2013
  • Let G = (V, E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V (G) and E = E(G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The distance between the vertices $u$ and $v$ in V (G) of graph G is the number of edges in a shortest path connecting them, we denote by $d(u,v)$. In graph theory, we have many invariant polynomials for a graph G. In this paper, we focus on the Schultz polynomial, Modified Schultz polynomial, Hosoya polynomial and their topological indices of a molecular graph circumcoronene series of benzenoid $H_k$ and specially third member from this family. $H_3$ is a basic member from the circumcoronene series of benzenoid and its conclusions are base calculations for the Schultz polynomial and Hosoya polynomial of the circumcoronene series of benzenoid $H_k$ ($k{\geq}3$).

A Study on Facility Layout Planning Using Graph Theory (그래프 이론을 이용한 설비배치 계획에 관한 연구)

  • Kim, Jae-Gon;Lee, Geun-Cheol;Kim, Yeong-Dae
    • Journal of Korean Institute of Industrial Engineers
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    • v.23 no.2
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    • pp.359-370
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    • 1997
  • We consider a facility layout problem with the objective of minimizing total transportation distance, which is the sum of rectilinear distances between facilities weighted by the frequency of trips between the facilities. It is assumed that facilities are required to have rectangular shapes and there is no empty space between the facilities in the layout. In this study, a graph theoretic heuristic is developed for the problem. In the heuristic, planar graphs are constructed to represent adjacencies between the facilities and then the graphs are converted to block layouts on a continual plane using a layout construction module. (Therefore, each graph corresponds to a layout.) An initial layout is obtained by constructing a maximal weighted planar graph and then the layout is improved by changing the planar graph. A simulated annealing algorithm is used to find a planar graph which gives the best layout. To show the performance of the proposed heuristic, computational experiments are done on randomly generated test problems and results are reported.

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SEMISYMMETRIC CUBIC GRAPHS OF ORDER 34p3

  • Darafsheh, Mohammad Reza;Shahsavaran, Mohsen
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.3
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    • pp.739-750
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    • 2020
  • A simple graph is called semisymmetric if it is regular and edge transitive but not vertex transitive. Let p be a prime. Folkman proved [J. Folkman, Regular line-symmetric graphs, Journal of Combinatorial Theory 3 (1967), no. 3, 215-232] that no semisymmetric graph of order 2p or 2p2 exists. In this paper an extension of his result in the case of cubic graphs of order 34p3, p ≠ 17, is obtained.

MODEL BASED DIAGNOSTICS FOR A GEARBOX USING INFORMATION THEORY

  • Choi, J.;Bryant, M.D.
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • pp.459-460
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    • 2002
  • This article discusses a diagnostics method based on models, and information theory. From an extensive system dynamics bond graph model of a gearbox [1], simulated were various cases germane to this diagnostics approach, including the response of an ideal gearbox, which functions perfectly to designer's specifications, and degraded gearboxes with tooth root cracking. By comparing these cases and constructing a signal flow analogy between the gearbox and a communication channel, Shannon' s information theory [2], including theorems, was applied to the gearbox to assess system health, in terms of ability to function.

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Applications of Graph Theory for the Pipe Network Analysis (상수관망해석을 위한 도학의 적용)

  • Park, Jae-Hong;Han, Geon-Yeon
    • Journal of Korea Water Resources Association
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    • v.31 no.4
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    • pp.439-448
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    • 1998
  • There are many methods to calculate steady-state flowrate in a large water distribution system. Linear method which analyzes continuity equations and energy equations simultaneously is most widely used. Though it is theoretically simple, when it is applied to a practical water distribution system, it produces a very sparse coefficient matrix and most of its diagonal elements are to be zero. This sparsity characteristic of coefficient matrix makes it difficult to analyze pipe flow using the linear method. In this study, a graph theory is introduced to water distribution system analysis in order to prevent from producing ill-conditioned coefficient matrix and the technique is developed to produce positive-definite matrix. To test applicability of developed method, this method is applied to 22 pipes and 142 pipes system located nearby Taegu city. The results obtained from these applications show that the method can calculate flowrate effectively without failure in converage. Thus it is expected that the method can analyze steady state flowrate and pressure in pipe network systems efficiently. Keywords : pipe flow analysis, graph theory, linear method.

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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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Shortest Path Problem in a Type-2 Fuzzy Weighted Graph (타입 2-퍼지 가중치 그래프에서 최단경로 문제)

  • 이승수;이광형
    • Journal of the Korean Institute of Intelligent Systems
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    • v.11 no.6
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    • pp.528-531
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    • 2001
  • Finding a shortest path on a graph is a fundamental problem in the area of graph theory. In an application where we cannot exactly determine the weights of edges fuzzy weights can be used instead of crisp weights. and Type-2 fuzzy weight will be more suitable of this uncertainty varies under some conditions. In this paper, shortest path problem in type-1 fuzzy weighted graphs is extended for type 2 fuzzy weighted graphes. A solution is also given based on possibility theory and extension principle.

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Shortest Path Problem in a Type-2 Fuzzy Weighted Graph (타입-2 퍼지 가중치 그래프에서의 최단경로문제)

  • Lee, Seungsoo;Lee, Kwang H.
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.314-318
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    • 2001
  • Constructing a shortest path on a graph is a fundamental problem in the area of graph theory. In an application where we cannot exactly determine the weights of edges, fuzzy weights can be used instead of crisp weights, and Type-2 fuzzy weights will be more suitable if this uncertainty varies under some conditions. In this paper, shortest path problem in type-1 fuzzy weighted graphs is extended for type-2 fuzzy weighted graphes. A solution is also given based on possibility theory and extension principle.

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A Study on Constructing the Multiple-Valued Logic Systems over Finite Fields using by the Decision Diagram (결정도(決定圖)에 기초(基礎)한 유한체상(有限體上)의 다치논리(多値論理)시스템구성(構成)에 관한 연구(硏究))

  • Park, Chun-Myoung
    • Journal of IKEEE
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    • v.3 no.2
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    • pp.295-304
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    • 1999
  • This paper presents a method of constructing the Multiple-Valued Logic Systems(MVLS) over Finite Fields(FF) using by Decision Diagram(DD) that is based on Graph Theory. The proposed method is as following. First, we derivate the Ordered Multiple-Valued Logic Decision Diagram(OMVLDD) based on the multiple-valued Shannon's expansion theorem and we execute function decomposition using by sub-graph. Next, we propose the variable selecting algorithm and simplification algorithm after apply the each isomorphism and reodering vertex. Also we propose MVLS design method.

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