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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 Introduction1.1 Locally-coconnected graphs1.2 Locally-connected graphs1.3 Asteroidal Triple1.4 Denition ξ(G); λ’(G); λ(G); δ(G)1.5 Restricted Edge Connectivity1.6 Super Restricted Edge Connected and Maximal Restricted Edge Connected2 Some properties of locally coconnected graphs and locally connected graphs2.1 Some properties of locally-coconnected graphs2.2 Some properties of locally-connected graphs3 Some properties of k-regular connected graph3.1 k-regular connected graph3.2 G is a k-regular connected graph3.3 Relation between ξ(G) and λ’(G)3.4 Relation between λ’(G) and λ(G)4 Some properties of of connected graphs 214.1 The maximum value of m′′ = ξ(G) − δ(G)4.2 The case when m′′ = n − 35 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 ConnectedGraphs. Casopls pro pestovani matematiky, roc. 99(1974), Praha.[3] Martin Charles Golumbic Ann N.Trenk. Tolerance Graphs. December6,2002.[4] Xu Jun-Ming , Xu Ke-Li . On Restricted Edge Connectivity ofGraphs. Discrete Mathematics 243(2002) 291-298.[5] Ou Jianping and Zhang Fuji . Super Restricted Edge Connectivityof Regular Graphs. Graphs and Combinatorics, 21 (2001) 459-467.[6] Hougardy Stefan. Classes of Perfect Graphs. DiscreteMathematics,V306,19-20, 6 October (2006) 2529-2571.
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