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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/36394
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dc.contributor.advisor張宜武zh_TW
dc.contributor.advisorChang, Yi-Wuen_US
dc.contributor.author曾煥絢zh_TW
dc.contributor.authorTseng, Huan-Hsuanen_US
dc.creator曾煥絢zh_TW
dc.creatorTseng, Huan-Hsuanen_US
dc.date1997en_US
dc.date.accessioned2009-09-18T10:28:17Z-
dc.date.available2009-09-18T10:28:17Z-
dc.date.issued2009-09-18T10:28:17Z-
dc.identifierB2002001695en_US
dc.identifier.urihttps://nccur.lib.nccu.edu.tw/handle/140.119/36394-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用數學研究所zh_TW
dc.description85751006zh_TW
dc.description86zh_TW
dc.description.abstract在張宜武教授的博士論文中研究到視線表示法和視線數。我們以類似的方法定義有向圖的表示法和有向圖的視線數。\r\n首先，我們定義有向圖的視線數為b(Ｄ) ，Ｄ為有方向性的圖，在論文中可得b(Ｄ)≦┌1/2max｛△﹢(Ｄ),△﹣(Ｄ)｝┐。另一個重要的結論為考慮一個平面有向圖Ｄ，對圖形Ｄ上所有的點v，離開點v的邊（進入的邊）是緊鄰在一起時，則可得有向圖的視線數在這圖形上是１（即 b(Ｄ)=1）。\r\n另外對特殊的圖形也有其不同的視線數，即對有向完全偶圖Ｄm,n ，b(Ｄm,n)≦┌1/2min｛m,n｝┐ ，而對競賽圖Ｄn ，可得b(Ｄn)≦┌n/3┐+1。zh_TW
dc.description.abstractIn [2], Chang stuidied the bar visibility representations and defined bar visibility number.We defined analogously the bar visibility representation and the bar visibility number of a directed graph Ｄ.\r\nFirst we show that the bar visibility number, denoted by b(Ｄ),is at most ┌1/2max｛△﹢(Ｄ),△﹣(Ｄ)｝┐ if D is an oriented graph.And we show that b(Ｄ)=1 for the oriented planar graphs in which all outgoing (incoming) edges of any vertex v of Ｄ appear consecutively around v.For any complete bipartite digraph Ｄm,n ，b(Ｄm,n)≦┌1/2min｛m,n｝┐.For any tournament Ｄn,b(Ｄn)≦┌n/3┐+1.en_US
dc.description.tableofcontentsContents\r\nABSTRACT\r\nChapter 0 INTRODUCTION….......………………………………………...........1\r\nChapter 1 BAR VISIBILITY NUMBER AND DEGREE…………....................4\r\n 1.1 Some basic results of b(D)………………………………..............4\r\n 1.2 S-T form Algorithm….....…………………………………...........7\r\nChapter 2 BAR VISIBILITY NUMBER OF ORIENTED PLANAR GRAPH14\r\n 2.1 Bar visibility Algorithm.………….....………………………......15\r\n 2.2 Bar visibility Algorithm of oriented planar graph………….........19\r\nChapter 3 BAR VISIBILITY NUMBER OF AND ............................24\r\nChapter 4 CONCLUSIONS………………………………………………….......28\r\nREFERENCES .....................................................................................................30zh_TW
dc.language.isoen_US-
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#B2002001695en_US
dc.subject有向圖zh_TW
dc.subjectoriented graphen_US
dc.subjectplanaren_US
dc.title有向圖的視線數zh_TW
dc.titleBar visibility number of oriented graphen_US
dc.typethesisen
dc.relation.referenceREFERENCESzh_TW
dc.relation.reference[1] J. A. Boundy and U. S. R. Murty, Graph theory with applications (1976).zh_TW
dc.relation.reference[2] Yi-Wu Chang, Bar visibility number, Ph.D. thesis, University of Illinois, 92-102, (1994).zh_TW
dc.relation.reference[3] S. Even, Graph Algorithms, Computer Science Press, Rockville, MD, (1979).zh_TW
dc.relation.reference[4] A. Lempel, S. Even, and I. Cederbaum, An algorithm for planarity testing of graphs, in Theory of Graphs (Proceedings of an International Symposium, Rome, July 1966), (P. Rosenstiehl, ed.), 215-232, Gordon and Breach, New York, (1967).zh_TW
dc.relation.reference[5] Y.-L. Lin and S.S. Skiena, Complexity aspects of visibility graphs, International journal of Computational Geometry & Applications.zh_TW
dc.relation.reference<br>[6] L. A. Melnikov, Problem at the Sixth Hungarian Colloquium on Combinatorics, Eger, (1981).zh_TW
dc.relation.reference[7] M. Schlag, F. Luccio, P. Maestrini, D. T. Lee, and C. K. Wong, A visibility problem in VLSI layout compaction, in Advances in Compution Research, Vol. 2 (F. P. Preparata, ed.), 259-282, JAI Press Inc.,Greenwich, CT, (1985).zh_TW
dc.relation.reference[8] M. Sen, S. Das, A.B. Roy, and D.B. West, Interval digraphs: An analogue of interval graphs, J. Graph Theory, Vol. 13, 189-202 (1989).zh_TW
dc.relation.reference[9] R. Tamassia and I. G. Tollis, A unified approach to visibility representations of planar graphs, Discrete and Computational Geometry, Vol. 1, 321-341 (1986).zh_TW
dc.relation.reference[10] D. B. West, Degrees and digraphs, Introduction to Graph Theory, 46-49, (1996).zh_TW
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