| 临界h-边-连通图的临界度 |
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| 引用本文： | 李永洁.临界h-边-连通图的临界度[J].应用数学,2008,21(1):59-66. |
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| 作者姓名： | 李永洁 |
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| 作者单位： | 华中科技大学,湖北,武汉,430074 |
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| 摘 要： | 图G称为k-临界h-边-连通的,若h=λ(G)且对每个k顶点集{u1,…,uk}有λ(G-{u1,…,ui})≤λ(G-{u1,…,ui-1})-1,I≤k.若G是k-临界h-边-连通但不(k 1)-临界h-边-连通,则记之为(h*,k*)λ.本文证明了:存在(h*,k*)λ图的充要条件是(1)1≤k≤(h 1)/2],h≡0,1,2(mod 4);1≤k≤(h-1)/2],h≡3(mod 4);或(2)k=h,G=Kk 1.
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| 关 键 词： | k-临界h-边连通图 临界度 控制集 k-critically h-edge-connected graph Criticality Dominating set 临界度 连通图 graph 条件 存在 顶点集 |
| 文章编号： | 1001-9847(2008)01-0059-08 |
| 修稿时间： | 2007年2月28日 |
On Criticality of Critically h-edge -connected Graphs |
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| LI Yong-jie.On Criticality of Critically h-edge -connected Graphs[J].Mathematica Applicata,2008,21(1):59-66. |
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| Authors: | LI Yong-jie |
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| Abstract: | A graph G is said to be k-critically h-edge-connected if λ(G)=h and for every set of k vertices {u1,...,uk},λ(G-{u1,...,ui})≤λ(G-{u1,...,ui-1})-1,i≤k.If G is k-critically h-edge-connected but not (k+1)-critically h-edge-connected,then we denote it by (h*,k*)λ-graph.It is proved that there exists an (h*,k*)λ-graph G,iff(i)1≤k≤(h+1)/2],h≡0,1,2(mod 4)and 1≤k≤(h-1)/2],h≡3 (mod 4) or (ii)k=h and G=Kh+1. |
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| Keywords: | k-critically h-edge-connected graph Criticality Dominating set |
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