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題名 有關對立圖形的探討
Some Problems on Opposition Graphs
作者 潘丞偉
貢獻者 張宜武
潘丞偉
關鍵詞 對立圖形
Opposition Graphs
日期 2012
上傳時間 1-Feb-2013 16:53:14 (UTC+8)
摘要 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.
參考文獻 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.
描述 碩士
國立政治大學
應用數學研究所
98751008
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0098751008
資料類型 thesis
dc.contributor.advisor 張宜武zh_TW
dc.contributor.author (Authors) 潘丞偉zh_TW
dc.creator (作者) 潘丞偉zh_TW
dc.date (日期) 2012en_US
dc.date.accessioned 1-Feb-2013 16:53:14 (UTC+8)-
dc.date.available 1-Feb-2013 16:53:14 (UTC+8)-
dc.date.issued (上傳時間) 1-Feb-2013 16:53:14 (UTC+8)-
dc.identifier (Other Identifiers) G0098751008en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/56876-
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) 98751008zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 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。zh_TW
dc.description.abstract (摘要) 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.		en_US
dc.description.tableofcontents 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		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0098751008en_US
dc.subject (關鍵詞) 對立圖形zh_TW
dc.subject (關鍵詞) Opposition Graphsen_US
dc.title (題名) 有關對立圖形的探討zh_TW
dc.title (題名) Some Problems on Opposition Graphsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 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.		zh_TW