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研究生:郭志銘
研究生(外文):Jyh-Min Kuo
論文名稱:互質圖的猜測
論文名稱(外文):On Prime Labeling Conjecture
指導教授:傅恆霖
指導教授(外文):Hung-Lin Fu
學位類別:碩士
校院名稱:國立交通大學
系所名稱:應用數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:29
中文關鍵詞:互質圖互質樹輪子
外文關鍵詞:prime labelingprime treewheelsprime labeling conjecture
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  • 收藏至我的研究室書目清單書目收藏:1
1980年左右Roger Entringer, 猜測『任何樹都可以互質標示』,廿幾年過去了,進展很小,主要的成果都是在一些特別的例子上標示,對實際的樹,幫助很小。這篇論文首先證明李信明等人的猜測:『很多輪子的集合可以互質標示』,然後證明這篇論文的主要定理『對任何點數小於17的樹,都可以用連續的數標示』;最後,利用這個定理對一般的樹,在一些要求下,給一互質標示。我們相信大部份的樹,都可以藉由這個方法全部加以標示。我們也期待用這個方法,很快地把原猜測解決。

In 1980, Roger Entringer conjectured: every tree has a prime labeling. So far, this conjecture is still unsolved. As a matter of fact, only some special types of trees are verified.
In this thesis, we first prove the conjecture by S. M. Lee. et al : the amalgamation of m copies of the wheel Wn that share common center, Wm,n, is prime provided that n is even.
Then, in section 2.2 we show the main theorem: every tree with order n(n 16) has a modified prime labeling by using consecutive n integers. Using this theorem we are able to show that more classes of trees are prime. We believe that the idea developed in this thesis can be applied to tackle the conjecture by Roger Entringer.

Abstract (in Chinese)
Abstract (in English)
Acknowledgment
Contents
Chapter 1 Preliminaries
1.1 Graph terms
1.2 Special types of graphs
1.3 The conjectures
1.4 The known results
Chapter 2 New Results
2.1 Amalgamation of two or more copies of the Wheels Wn
2.2 Modified labeling of small trees
Appendix
Reference

[1] D. B. West, Introduction to Graph Theory, Prentice Hall (in 1996).
[2] H. Salmasian, A result on the prime labeling of trees, Bulletin of the ICA, Vol. 28, Jan., 2000, 36-38..
[3] Hung-Lin Fu and Kuo-Ching Huang, On prime labeling, Discrete Math, 127(1994) 181-186
[4] M. A. Seoud, A. T. Diab and E. A. Elsahawi, On strongly c-harmoniours, cordial, prime labeling and odd graceful graphs, in preprint.
[5] M. A. Seoud and M. Z. Youssef, On prime labeling of graphs, Congressus Numerantium 141 (1999) 203-215.
[6] S. H. Lin., A study of prime labeling, M. Sc. Thesis, National Chiao Tung University, 1998.
[7] S. M. Lee, I. Wui and J. Yeh, On the amalgamation of prime graphs, Bull. Malaysian Math. Soc. (2) 11 (1988)59-67.
[8] T. Deretsky, S. M. Lee and J. Mitchem, On vertex prime labeling of graphs, in Graph Theroy, Combinatorics and Applications Vol. 1, J. Alavi, G. Chartrand,
O. Oellerman and A. Schwenk, eds., Proceedings 6th International Conference Theory and Applications of Graphs (Wiley, New York, 1991) 356-369.
[9] T. Nicholas, Classes of prime labeled graphs, in preprints.

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