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研究生:陳欣玫
論文名稱:K-regular graphs edges connectivity and related topics
論文名稱(外文):K規則圖的線連通之探討
指導教授:林英仁
指導教授(外文):In-Jen Lin
學位類別:碩士
校院名稱:國立臺灣海洋大學
系所名稱:資訊工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:英文
論文頁數:30
中文關鍵詞:局部反連通圖局部連通圖K規則圖
外文關鍵詞:locally coconnectedlocally connectedK-regular graphs
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首先,我們探討有關於局部反連通圖和局部連通圖的特性,接下來我們做一些問題有關於下列參數,m = ξ(G) - λ’(G),m’= λ’(G)- λ(G),m’’ = ξ(G) - δ(G)。最後,在得到極值時線段數不大於2n-4。


We found some properties for the locally coconnected and locally connected. And some problems on the parameter of m = ξ(G) - λ’(G), m’= λ’(G)- λ(G), and m’’ = ξ(G) - δ(G) then finally with extremal case, we have E(G) ≧ 2n – 4.


1 Introduction
1.1 Locally-coconnected graphs
1.2 Locally-connected graphs
1.3 Asteroidal Triple
1.4 Denition ξ(G); λ’(G); λ(G); δ(G)
1.5 Restricted Edge Connectivity
1.6 Super Restricted Edge Connected and Maximal Restricted Edge Connected
2 Some properties of locally coconnected graphs and locally connected graphs
2.1 Some properties of locally-coconnected graphs
2.2 Some properties of locally-connected graphs
3 Some properties of k-regular connected graph
3.1 k-regular connected graph
3.2 G is a k-regular connected graph
3.3 Relation between ξ(G) and λ’(G)
3.4 Relation between λ’(G) and λ(G)
4 Some properties of of connected graphs 21
4.1 The maximum value of m′′ = ξ(G) − δ(G)
4.2 The case when m′′ = n − 3
5 Conclusion
[1] E. G. Kohler. Graphs without Asteroidal Triples. PhD thesis,
Technische Universitat Berlin, Cuvillier Verlag Gottingen, 1999.
[2] Chartrand Gary and Pippert Raymond E. Locally Connected
Graphs. Casopls pro pestovani matematiky, roc. 99(1974), Praha.
[3] Martin Charles Golumbic Ann N.Trenk. Tolerance Graphs. December
6,2002.
[4] Xu Jun-Ming , Xu Ke-Li . On Restricted Edge Connectivity of
Graphs. Discrete Mathematics 243(2002) 291-298.
[5] Ou Jianping and Zhang Fuji . Super Restricted Edge Connectivity
of Regular Graphs. Graphs and Combinatorics, 21 (2001) 459-467.
[6] Hougardy Stefan. Classes of Perfect Graphs. Discrete
Mathematics,V306,19-20, 6 October (2006) 2529-2571.
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