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研究生:林耀仁
研究生(外文):Yao-ren Lin
論文名稱:圖的IC-著色之研究
論文名稱(外文):A Study of IC-coloring of Graphs
指導教授:江南波
指導教授(外文):Nam-po Chiang
學位類別:碩士
校院名稱:大同大學
系所名稱:應用數學學系(所)
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:2008
畢業學年度:96
語文別:英文
論文頁數:38
中文關鍵詞:IC-指數可和飽和圖IC-著色
外文關鍵詞:IC-coloringsum-saturableIC-index
相關次數:
  • 被引用被引用:0
  • 點閱點閱:160
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  • 下載下載:6
  • 收藏至我的研究室書目清單書目收藏:0
在這篇論文中,第二章我們探討所有小於或等於九個頂點的不同構的樹狀圖的和飽和性,且證明出對於每個n 2的完美完全n元樹是可和飽和圖。第三章我們得到Kn-2e, Kn-3e 及完全三分圖的IC-指數的上、下界。
In this thesis, we study thoroughly the sum-saturability of all non-isomorphic trees of order less than or equal to 9, and we also prove that, for each n 2, the perfect complete n-ary tree is sum-saturable in Chapter 2. And also we study the bounds for the IC-indices of Kn-2e, Kn-3e and complete tripartite graphs in Chapter 3.
ACKNOWLEDGMENTS i
ENGLISH ABSTRACT ii
CHINESE ABSTRACT iii
TABLE OF CONTENTS iv
LIST OF FIGURES vi
LIST OF TABLES vii
CHAPTER
1 Introduction 1

1.1 Preliminaries 2
1.2 Sum-saturable 5
1.3 IC-coloring 5

2.Sum-saturability of Trees 7

2.1 Tree with at most 9 Vertices 7
2.2 The Complete n-ary Trees 22

3.IC-indice Of SomeGraphs 26
3.1 IC-index of Kn-2e 26
3.2 IC-index of Kn-3e 28
3.3 IC-index of Complete Tripartite Km,n,p 35

4.Conclusion 36
REFERENCES 37
[1] B. Bolt. Mathematical Cavalcade, Cambridge University
Press, Cambridge, 1992.

[2] Douglas. B. West (2001), Introduction to Graph Theory,
Upper Saddle River, NJ 07458: Prentice Hall.

[3] J. A. Bondy and U. S. R. Murty(1976), Graph Theory with
Applications, Macmillan,North-Holland: New York, Amsterdam, Oxford.

[4] J.F. Fink, Labelings that realize connected subgraphs of
all conceivable values,
Congressus Numerantium, 132(1998), pp.29-37.

[5] S.G. Penrice, Some new graph labeling problem: a
preliminary report, DIMACS Tech. Rep. 95-26(1995), pp.1-9.

[6] E. Salehi, S. Lee and M. Khatirinejad, IC-Colorings and
IC-Indices of graphs, Discrete Mathematics, 299(2005), pp. 297-310.

[7] Chin-Lin Shiue and Hung-Lin Fu, The IC-Indices of
Complete Bipartite Graphs, Electronic J. of Combinatorics, 15(2008)
R43.

[8] Nam-Po Chiang and Shi-Zuo Lin, IC-Colorings of the Join
and the Combination of graphs,Master of Science Institute of Applied
Mathematics Tatung University, July 2007.

[9] Bao-Gen Xu, On IC-colorings of Connected Graphs, Journal
of East China Jiaotong University, Vol.23 No.1 Feb, 2006.

[10] Hung-Lin Fu and Chun-Chuan Chou, A Study of Stamp
Problem, Department of Applied Mathematics College of Science
National Chiao Tung University , June 2007.

[11] R. Alter, J.A. Barnett, A postage stamp problem, Amer.
Math. Monthly 87(1980), pp.206-210.

[12] R. Guy, The Postage Stamp Problem, Unsolved Problems in
Number Theory, second ed., Springer, New York, 1994, pp.123-127.

[13] R.L. Heimer, H. Langenbach, The stamp problem, J.
Recreational Math. 7 (1974), pp.235-250.

[14] W.F. Lunnon, A postage stamp problem, Comput. J.
12(1969), pp.377-380.
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