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| 研究生： |
陳玫芳 |
|---|---|
| 論文名稱： |
關於邊連通數和邊度數的問題 Some topics on edge connectivity and edge degrees |
| 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： | 2011 |
| 畢業學年度： | 99 |
| 語文別： | 英文 |
| 論文頁數： | 29 |
| 中文關鍵詞： | 局部連通圖 、邊切集 、限制邊連通數 |
| 外文關鍵詞： | Locally Connected Graphs, Edge Cuts, Restricted Edge Connectivity |
| 相關次數： | 點閱：139 下載：34 |
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在這篇論文中，我們根據局部連通和局部補連通性質將圖分類，計算在 Harary 圖裡大小為 2k - 1 和 2k 邊切集的個數，和證明當圖形有最大的最小邊度數和最小點度數差，一些關於度數為 1 的點個數性質。
In this thesis, we classify some graphs into locally coconnected graphs or locally connected graphs, compute the number of its edge cuts of size 2k - 1 and 2k in a Harary graph, and show some properties of the number of vertices of degree 1 when the graph has the maximum difference of minimum edge degree and minimum vertex degree.
Abstract ii
中文摘要 iii
1 Introduction 1
2 Some Properties of Locally Connected Graphs and Locally Coconnected Graphs 2
3 The Number of Edge Cuts of k-regular Graphs 7
4 The Maximum Di fference of the Minimum Edge Degree and the
Minimum Vertex Degree of a Graph 23
5 Open Problems and Further Directions of Studies 28
References 29
[1] A.-H. Esfahanian and S. L. Hakimi, On computing a conditional edge-connectivity of a graph, Information Processing Letters, 27 (1988), pp. 195-199.
[2] O. Jianping and F. Zhang, Super restricted edge connectivity of regular graphs, Graphs and Combinatorics, 21 (2005), pp. 459-467.
[3] E. G. Kohler, Graphs Without Asteroidal Triples, PhD thesis, Technischen Universitat Berlin, 1999.
[4] D. B. West, Introduction to Graph Theory, Prentice Hall, 2001.
[5] J.-M. Xu and K.-L. Xu, On restricted edge-connectivity of graph, Discrete Mathematics, 243 (2002), pp. 291-298.
