• Title, Summary, Keyword: order of a graph

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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.

ON THE MINIMUM ORDER OF 4-LAZY COPS-WIN GRAPHS

  • Sim, Kai An;Tan, Ta Sheng;Wong, Kok Bin
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1667-1690
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    • 2018
  • We consider the minimum order of a graph G with a given lazy cop number $c_L(G)$. Sullivan, Townsend and Werzanski [7] showed that the minimum order of a connected graph with lazy cop number 3 is 9 and $k_3{\square}k_3$ is the unique graph on nine vertices which requires three lazy cops. They conjectured that for a graph G on n vertices with ${\Delta}(G){\geq}n-k^2$, $c_L(G){\leq}k$. We proved that the conjecture is true for k = 4. Furthermore, we showed that the Petersen graph is the unique connected graph G on 10 vertices with ${\Delta}(G){\leq}3$ having lazy cop number 3 and the minimum order of a connected graph with lazy cop number 4 is 16.

CHARACTERIZATION THEOREMS FOR CERTAIN CLASSES OF INFINITE GRAPHS

  • Jung, Hwan-Ok
    • Journal of applied mathematics & informatics
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    • v.30 no.1_2
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    • pp.245-252
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    • 2012
  • In this paper we present a necessary and sufficient conditions for an infinite VAP-free plane graph to be a 3LV-graph as well as an LV-graph. We also introduce and investigate the concept of the order and the kernel of an infinite connected graph containing no one-way infinite path.

Efficient Dynamic Object-Oriented Program Slicing

  • Park, Soon-Hyung;Park, Man-Gon
    • Journal of Korea Multimedia Society
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    • v.6 no.4
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    • pp.736-745
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    • 2003
  • Traditional slicing techniques make slices through dependence graphs. They also improve the accuracy of slices. However, traditional slicing techniques require many vertices and edges in order to express a data communication link because they are based on static slicing techniques. Therefore the graph becomes very complicated, and size of the slices is larger. We propose the representation of a dynamic object-oriented program dependence graph so as to process the slicing of object-oriented programs that is composed of related programs in order to process certain jobs. We also propose an efficient slicing algorithm using the relations of relative tables in order to compute dynamic slices of object-oriented programs. Consequently, the efficiency of the proposed efficient dynamic object-oriented program dependence graph technique is also compared with the dependence graph techniques discussed previously As a result, this is certifying that an efficient dynamic object-oriented program dependence graph is more efficient in comparison with the traditional object-oriented dependence graphs and dynamic object-oriented program dependence graph.

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Improving the I/O Performance of Disk-Based Graph Engine by Graph Ordering (디스크 기반 그래프 엔진의 입출력 성능 향상을 위한 그래프 오더링)

  • Lim, Keunhak;Kim, Junghyun;Lee, Eunjae;Seo, Jiwon
    • KIISE Transactions on Computing Practices
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    • v.24 no.1
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    • pp.40-45
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    • 2018
  • With the advent of big data and social networks, large-scale graph processing becomes popular research topic. Recently, an optimization technique called Gorder has been proposed to improve the performance of in-memory graph processing. This technique improves performance by optimizing the graph layout on memory to have better cache locality. However, since it is designed for in-memory graph processing systems, the technique is not suitable for disk-based graph engines; also the cost for applying the technique is significantly high. To solve the problem, we propose a new graph ordering called I/O Order. I/O Order considers the characteristics of I/O accesses for SSDs and HDDs to improve the performance of disk-based graph engine. In addition, the algorithmic complexity of I/O Order is simple compared to Gorder, hence it is cheaper to apply I/O Ordering. I/O order reduces the cost of pre-processing up to 9.6 times compared to that of Gorder's, still its performance is 2 times higher compared to the Random in low-locality graph algorithms.

Dynamic Slicing using Dynamic System Dependence Graph (동적 시스템 종속 그래프를 사용한 동적 슬라이싱)

  • 박순형;박만곤
    • Journal of Korea Multimedia Society
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    • v.5 no.3
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    • pp.331-341
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    • 2002
  • Traditional slicing techniques make slices through dependence graph and improve the accuracy of slices. However, traditional slicing techniques require many vertices and edges in order to express a data communication link because they are based on static slicing techniques. Therefore the graph becomes very complicated. We propose the representation of a dynamic system dependence graph so as to process the slicing of a software system that is composed of related programs in order to process certain jobs. We also propose programs on efficient slicing algorithm using relations of relative tables in order to compute dynamic slices of a software system. Using a marking table from results of the proposed algorithm can make dynamic system dependence graph for dynamic slice generation. Tracing this graph can generate final slices. We have illustrated our example with C program environment. Consequently, the efficiency of the proposed dynamic system dependence graph technique is also compared with the dependence graph techniques discussed previously. As the results, this is certifying that the dynamic system dependence graph is more efficient in comparison with system dependence graph.

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Efficient Dynamic Slicing of Object-Oriented Program

  • Park, Soon-Hyung
    • Proceedings of the Korea Society for Industrial Systems Conference
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    • pp.651-655
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    • 2008
  • Traditional slicing techniques make slices through dependence graphs. They also improve the accuracy of slices. However, traditional slicing techniques require many vertices and edges in order to express a data communication links. Therefore the graph becomes complicated, and size of the slices is larger. We propose the representation of a dynamic object-oriented program dependence graph so as to process the slicing of object-oriented programs that is composed of related programs in order to process certain jobs. The efficiency of the proposed efficient dynamic object-oriented program dependence graph technique is also compared with the dependence graph techniques discussed previously. As a result, this is certifying that an efficient dynamic object-oriented program dependence graph is more efficient in comparison with the traditional dynamic object-oriented program dependence graph.

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A Genetic Algorithm for Directed Graph-based Supply Network Planning in Memory Module Industry

  • Wang, Li-Chih;Cheng, Chen-Yang;Huang, Li-Pin
    • Industrial Engineering and Management Systems
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    • v.9 no.3
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    • pp.227-241
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    • 2010
  • A memory module industry's supply chain usually consists of multiple manufacturing sites and multiple distribution centers. In order to fulfill the variety of demands from downstream customers, production planners need not only to decide the order allocation among multiple manufacturing sites but also to consider memory module industrial characteristics and supply chain constraints, such as multiple material substitution relationships, capacity, and transportation lead time, fluctuation of component purchasing prices and available supply quantities of critical materials (e.g., DRAM, chip), based on human experience. In this research, a directed graph-based supply network planning (DGSNP) model is developed for memory module industry. In addition to multi-site order allocation, the DGSNP model explicitly considers production planning for each manufacturing site, and purchasing planning from each supplier. First, the research formulates the supply network's structure and constraints in a directed-graph form. Then, a proposed genetic algorithm (GA) solves the matrix form which is transformed from the directed-graph model. Finally, the final matrix, with a calculated maximum profit, can be transformed back to a directed-graph based supply network plan as a reference for planners. The results of the illustrative experiments show that the DGSNP model, compared to current memory module industry practices, determines a convincing supply network planning solution, as measured by total profit.

ON THE MONOPHONIC NUMBER OF A GRAPH

  • Santhakumaran, A.P.;Titus, P.;Ganesamoorthy, K.
    • Journal of applied mathematics & informatics
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    • v.32 no.1_2
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    • pp.255-266
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    • 2014
  • For a connected graph G = (V,E) of order at least two, a set S of vertices of G is a monophonic set of G if each vertex v of G lies on an x - y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is the monophonic number of G, denoted by m(G). Certain general properties satisfied by the monophonic sets are studied. Graphs G of order p with m(G) = 2 or p or p - 1 are characterized. For every pair a, b of positive integers with $2{\leq}a{\leq}b$, there is a connected graph G with m(G) = a and g(G) = b, where g(G) is the geodetic number of G. Also we study how the monophonic number of a graph is affected when pendant edges are added to the graph.