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 Title: 4-Caterpillars的優美標法Graceful Labelings of 4-Caterpillars Authors: 吳文智Wu, Wen Chih Contributors: 李陽明吳文智Wu, Wen Chih Keywords: 樹優美圖Treesgraceful labelling4-Caterpillars4-stars Date: 2005 Issue Date: 2009-09-17 13:46:05 (UTC+8) Abstract: 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. Reference: [1] R.E. Aldred and B.D. McKay, Graceful and harmoniouslabellings 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9175100994 Source URI: http://thesis.lib.nccu.edu.tw/record/#G0091751009 Data Type: thesis Appears in Collections: [應用數學系] 學位論文

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