阶较小时具有最大棱数的极小k棱连通图MINIMALLY k-LINE-CONNECTED GRAPHS OF LOW ORDER WITH MAXIMAL SIZE
苏健基
摘要(Abstract):
设 G 是极小 k 棱连通图,|G|=n.Mader 已证明,当 k≥2,n≥3k 时,e(G)≤k(n-k),且 e(G)=k(n-k)的充要条件为 G=K~(k,(n-k)).当 k≥2,k+2≤n<3k时,我们得到 e(G)≤(n+k)~2/8,并给出 e(G)=(n+k)~2/8时图的结构.就其作用来说,本文所获得的结果与蔡茂诚关于极小 k 连通图的结果相似.
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作者(Author): 苏健基
参考文献(References):
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- [2] B.Bollobás,Springer-Verlag,Graph Theory an Introductory Course.New York,1979.
- [3] D.R.Lick,Minimally n-line Connected Graphs,J.Reine Angew.Math.252(1972) 178-182.
- [4] Cai Maocheng,Minimally k-connected Graphs of low Order and Maximal Size Discrete Mathematics.41(1982) 229-234.