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| Title | 4-Caterpillars的優美標法 Graceful Labelings of 4-Caterpillars |
| Creator | 吳文智 Wu, Wen Chih |
| Contributor | 李陽明 吳文智 Wu, Wen Chih |
| Key Words | 樹 優美圖 Trees graceful labelling 4-Caterpillars 4-stars |
| Date | 2005 |
| Date Issued | 17-Sep-2009 13:46:05 (UTC+8) |
| Summary | 樹是一個沒有迴路的連接圖。而4-caterpillar是一種樹，它擁有單一路徑連接到數個長度為3的路徑的端點。一個有n個邊的無向圖G的優美標法是一個從G的點到{0,1,2,...,n}的一對一函數，使得每一個邊的標號都不一樣，其中，邊的標號是兩個相鄰的點的編號差的絕對值。在這篇論文當中，我們最主要的目的是使用一個演算法來完成4-caterpillars的優美標法。 A tree is connected acyclic graph. A 4-caterpillar is a tree with a single path only incident to the end-vertices of paths of length 3. A graceful labelling of an undirected graph G with n edges is a one-to-one function from the set of vertices of G to the set {0,1,2,...,n} such that the induced edge labels are all distinct, where the edge label is the difference between two endvertex labels. In this thesis, our main purpose is to use an algorithm to yield graceful labellings of 4-caterpillars. |
| 參考文獻 | [1] R.E. Aldred and B.D. McKay, Graceful and harmonious labellings of trees, Bull. Inst. Combin. Appl., 23 (1998) 69-72. [2] R.E. Aldred, J. Siran and M. Siran, A Note on the number of graceful labellings of paths, Discrete Math., 261 (2003) 27-30. [3] J.C. Bermond, Graceful graphs, radio antennae and French windmills, Graph Theory and Combinatorics, Pitman, London (1979) 18-37. [4] J.C. Bermond and D. Sotteau, Graph decompositions and G-design, Proc. 5th British Combinatorics Conference, 1975, Congress. Number., XV (1976) 53-72. [5] V. Bhat-Nayak and U. Deshmukh, New families of graceful banana trees, Proc. Indian Acad. Sci Math. Sci., 106 (1996) 201-216. [6] G. S. Bloom, A chronology of the Ringel-Kotzig conjecture and the continuing quest to call all trees graceful, Ann. N. Y. Acad. Sci., 326 (1979) 32-51. [7] C.P. Bonnington and J. Siran, Bipartite labelling of trees with maximum degree three, Journal of Graph Theory, 31 (1999) 37-56. [8] L. Brankovic, A. Rose and J. Siran, Labelling of trees with maximum degree three and improved bound, preprint, (1999). [9] H.J. Broersma and C. Hoede, Another equivalent of the graceful tree conjecture, Ars Combinatoria, 51 (1999) 183-192. [10] M. Burzio and G. Ferrarese, The subdivision graph of a graceful tree is a graceful tree, Discrete Mathematices, 181 (1998) 275-281. [11] I. Cahit, R. Cahit, On the graceful numbering of spanning trees, Information Processing Letters, vol. 3, no. 4, pp. (1998) 115-118. [12] Y.-M. Chen, Y.-Z. Shih, 2-Caterpillars are graceful. Preprint, (2006). [13] W.C. Chen, H.I. Lu and Y.N. Yeh, Operations of interlaced trees and graceful trees, Southeast Asian Bulletin of Mathematics, 21 (1997) 337-348. [14] P. Hrnciar, A. Havier, All trees of diameter five are graceful. Discrete Mathematices, 31 (2001) 279-292. [15] K.M. Koh, D.G. Rogers and T. Tan, A graceful arboretum: A survey of graceful trees, in Proceedings of Franco-Southeast Asian Conference, Singapore, May 1979, 2 278-287. [16] D. Morgan, Graceful labelled trees from Skolem sequences, Proc. of the Thirty-first Southeastern Internat, Conf, on Combin., Graph Theory, Computing (Boca Raton, FL, 2000) and Congressus Numerantium, (2000) 41-48. [17] D. Morgan, All lobsters with perfect matchings are graceful, Electronic Notes in Discrete Mathematices, 11 (2002), 503-508. [18] A.M. Pastel and H. Raynaud, Les oliviers sont gracieux, Colloq. Grenoble, Publications Universite de Grenoble, (1978). [19] A. Rose, On certain valuations of the vertices of graph, Theory of Graphs, International Symposium, Rome, July 1996, Gordon and Breach, N.Y. and Dunod Paris (1967) 349-355. [20] J.-G. Wang, D.J. Jin, X.-G. Lu and D. Zhang, The gracefulness of a class of lobster Trees, Mathematical Computer Modelling, 20 (1994) 105-110. [21] D.B. West, Introduction to Graph Theory, Prentice-Hall, Inc. (1996). |
| Description | 碩士 國立政治大學 應用數學研究所 91751009 94 |
| 資料來源 | http://thesis.lib.nccu.edu.tw/record/#G0091751009 |
| Type | thesis |
| dc.contributor.advisor | 李陽明 | zh_TW |
| dc.contributor.author (Authors) | 吳文智 | zh_TW |
| dc.contributor.author (Authors) | Wu, Wen Chih | en_US |
| dc.creator (作者) | 吳文智 | zh_TW |
| dc.creator (作者) | Wu, Wen Chih | en_US |
| dc.date (日期) | 2005 | en_US |
| dc.date.accessioned | 17-Sep-2009 13:46:05 (UTC+8) | - |
| dc.date.available | 17-Sep-2009 13:46:05 (UTC+8) | - |
| dc.date.issued (上傳時間) | 17-Sep-2009 13:46:05 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0091751009 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/32569 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學研究所 | zh_TW |
| dc.description (描述) | 91751009 | zh_TW |
| dc.description (描述) | 94 | zh_TW |
| dc.description.abstract (摘要) | 樹是一個沒有迴路的連接圖。而4-caterpillar是一種樹，它擁有單一路徑連接到數個長度為3的路徑的端點。一個有n個邊的無向圖G的優美標法是一個從G的點到{0,1,2,...,n}的一對一函數，使得每一個邊的標號都不一樣，其中，邊的標號是兩個相鄰的點的編號差的絕對值。在這篇論文當中，我們最主要的目的是使用一個演算法來完成4-caterpillars的優美標法。 | zh_TW |
| dc.description.abstract (摘要) | A tree is connected acyclic graph. A 4-caterpillar is a tree with a single path only incident to the end-vertices of paths of length 3. A graceful labelling of an undirected graph G with n edges is a one-to-one function from the set of vertices of G to the set {0,1,2,...,n} such that the induced edge labels are all distinct, where the edge label is the difference between two endvertex labels. In this thesis, our main purpose is to use an algorithm to yield graceful labellings of 4-caterpillars. | en_US |
| dc.description.tableofcontents | 書名頁 謝辭 英文摘要 中文摘要 目次 第一章 Introduction 第二章 Main result 第三章 Further studies in the future 參考文獻 | zh_TW |
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| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0091751009 | en_US |
| dc.subject (關鍵詞) | 樹 | zh_TW |
| dc.subject (關鍵詞) | 優美圖 | zh_TW |
| dc.subject (關鍵詞) | Trees | en_US |
| dc.subject (關鍵詞) | graceful labelling | en_US |
| dc.subject (關鍵詞) | 4-Caterpillars | en_US |
| dc.subject (關鍵詞) | 4-stars | en_US |
| dc.title (題名) | 4-Caterpillars的優美標法 | zh_TW |
| dc.title (題名) | Graceful Labelings of 4-Caterpillars | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | [1] R.E. Aldred and B.D. McKay, Graceful and harmonious | zh_TW |
| dc.relation.reference (參考文獻) | labellings of trees, Bull. Inst. Combin. Appl., 23 (1998) 69-72. | zh_TW |
| dc.relation.reference (參考文獻) | [2] R.E. Aldred, J. Siran and M. Siran, A Note on the number of graceful labellings of paths, Discrete Math., 261 (2003) 27-30. | zh_TW |
| dc.relation.reference (參考文獻) | [3] J.C. Bermond, Graceful graphs, radio antennae and French windmills, Graph Theory and Combinatorics, Pitman, London (1979) 18-37. | zh_TW |
| dc.relation.reference (參考文獻) | [4] J.C. Bermond and D. Sotteau, Graph decompositions and G-design, Proc. 5th British Combinatorics Conference, 1975, Congress. Number., XV (1976) 53-72. | zh_TW |
| dc.relation.reference (參考文獻) | [5] V. Bhat-Nayak and U. Deshmukh, New families of graceful banana trees, Proc. Indian Acad. Sci Math. Sci., 106 (1996) 201-216. | zh_TW |
| dc.relation.reference (參考文獻) | [6] G. S. Bloom, A chronology of the Ringel-Kotzig conjecture and the continuing quest to call all trees graceful, Ann. N. Y. Acad. Sci., 326 (1979) 32-51. | zh_TW |
| dc.relation.reference (參考文獻) | [7] C.P. Bonnington and J. Siran, Bipartite labelling of trees with maximum degree three, Journal of Graph Theory, 31 (1999) 37-56. | zh_TW |
| dc.relation.reference (參考文獻) | [8] L. Brankovic, A. Rose and J. Siran, Labelling of trees with maximum degree three and improved bound, preprint, (1999). | zh_TW |
| dc.relation.reference (參考文獻) | [9] H.J. Broersma and C. Hoede, Another equivalent of the graceful tree conjecture, Ars Combinatoria, 51 (1999) 183-192. | zh_TW |
| dc.relation.reference (參考文獻) | [10] M. Burzio and G. Ferrarese, The subdivision graph of a graceful tree is a graceful tree, Discrete Mathematices, 181 (1998) 275-281. | zh_TW |
| dc.relation.reference (參考文獻) | [11] I. Cahit, R. Cahit, On the graceful numbering of spanning trees, Information Processing Letters, vol. 3, no. 4, pp. (1998) 115-118. | zh_TW |
| dc.relation.reference (參考文獻) | [12] Y.-M. Chen, Y.-Z. Shih, 2-Caterpillars are graceful. Preprint, (2006). | zh_TW |
| dc.relation.reference (參考文獻) | [13] W.C. Chen, H.I. Lu and Y.N. Yeh, Operations of interlaced trees and graceful trees, Southeast Asian Bulletin of Mathematics, 21 (1997) 337-348. | zh_TW |
| dc.relation.reference (參考文獻) | [14] P. Hrnciar, A. Havier, All trees of diameter five are graceful. Discrete Mathematices, 31 (2001) 279-292. | zh_TW |
| dc.relation.reference (參考文獻) | [15] K.M. Koh, D.G. Rogers and T. Tan, A graceful arboretum: A survey of graceful trees, in Proceedings of Franco-Southeast Asian Conference, Singapore, May 1979, 2 278-287. | zh_TW |
| dc.relation.reference (參考文獻) | [16] D. Morgan, Graceful labelled trees from Skolem sequences, Proc. of the Thirty-first Southeastern Internat, Conf, on Combin., Graph Theory, Computing (Boca Raton, FL, 2000) and Congressus Numerantium, (2000) 41-48. | zh_TW |
| dc.relation.reference (參考文獻) | [17] D. Morgan, All lobsters with perfect matchings are graceful, Electronic Notes in Discrete Mathematices, 11 (2002), 503-508. | zh_TW |
| dc.relation.reference (參考文獻) | [18] A.M. Pastel and H. Raynaud, Les oliviers sont gracieux, Colloq. Grenoble, Publications Universite de Grenoble, (1978). | zh_TW |
| dc.relation.reference (參考文獻) | [19] A. Rose, On certain valuations of the vertices of graph, Theory of Graphs, International Symposium, Rome, July 1996, Gordon and Breach, N.Y. and Dunod Paris (1967) 349-355. | zh_TW |
| dc.relation.reference (參考文獻) | [20] J.-G. Wang, D.J. Jin, X.-G. Lu and D. Zhang, The gracefulness of a class of lobster Trees, Mathematical Computer Modelling, 20 (1994) 105-110. | zh_TW |
| dc.relation.reference (參考文獻) | [21] D.B. West, Introduction to Graph Theory, Prentice-Hall, Inc. (1996). | zh_TW |