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| 研究生： |
潘丞偉 |
|---|---|
| 論文名稱： |
有關對立圖形的探討 Some Problems on Opposition Graphs |
| 指導教授： | 張宜武 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2013 |
| 畢業學年度： | 101 |
| 語文別： | 中文 |
| 論文頁數： | 29 |
| 中文關鍵詞： | 對立圖形 |
| 外文關鍵詞： | Opposition Graphs |
| 相關次數： | 點閱：178 下載：4 |
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在這篇論文中，我們探討對立圖形的特性，並藉由度數大於等於三的點，判斷一樹是否為對立圖形，最後證明Pn, Cn n ≥ 3 且 n = 4k; k ∈ N 家族的圖是對立圖形且Tn, Cn n ≥ 3 且n ̸= 4k; k ∈ N 家族的圖是對立圖形。
In this thesis, we use the number of vertices with degree greater than or equal to 3 as a criterion for trees being opposition graphs. Finally, we prove some families of graphs such as Pn, Cn with n ≥ 3 and n = 4k; k ∈ N are opposition graphs and some families of graphs such as Tn,
Cn with n ≥ 3 and n ̸= 4k; k ∈ N are not opposition graphs.
Contents
Abstract ii
中文摘要iii
1 Introduction 1
2 Definitions 3
3 Some Opposition Graphs 7
3.1 R(T) = ∅ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 There Are Only One Vertex u in R . . . . . . . . . . . . . . . . . . 11
3.3 There Are Two Vertices u,v in R(T) . . . . . . . . . . . . . . . . . 16
3.4 There Are More Than Two Vertices in R . . . . . . . . . . . . . . . 22
4 Some Families of Opposition Graphs 24
5 Open Problems and Further Directions of Studies 28
References 29
i
References
[1] A. N. Trenk, Tolerance Graphs, Cambridge Univ Pr, 2004.
[2] A. Tucker, Applied Combinatorics, Wiley, 2006.
[3] D. B. West, Introduction to Graph Theory, Prentice Hall, 2001.
