| Optimization problems of the third edge-connectivity of graphs |
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| 作者姓名： | WANG Yingqian |
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| 作者单位： | WANG Yingqian Department of Mathematics，Zhejiang Normal University，Jinhua，321004，China |
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| 基金项目： | 中国科学院资助项目;浙江省自然科学基金 |
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| 摘 要： | The third edge-connectivity λ3(G) of a graph G is defined as the minimum cardinality over all sets of edges, if any, whose deletion disconnects G and each component of the resulting graph has at least 3 vertices. An upper bound has been established for λ3(G) whenever λ3(G) is well-defined. This paper first introduces two combinatorial optimization concepts, that is, maximality and superiority, of λ3(G), and then proves the Ore type sufficient conditions for G to be maximally and super third edge-connected. These concepts and results are useful in network reliability analysis.
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| 收稿时间： | 15 August 2005 |
| 修稿时间： | 8 October 2005 |
Optimization problems of the third edge-connectivity of graphs |
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| WANG Yingqian.Optimization problems of the third edge-connectivity of graphs[J].Science in China(Mathematics),2006,49(6):791-799. |
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| Authors: | WANG Yingqian |
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| Institution: | Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China |
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| Abstract: | The third edge-connectivity λ3(G) of a graph G is defined as the minimum cardinality over all sets of edges, if any, whose deletion disconnects G and each component of the resulting graph has at least 3 vertices. An upper bound has been established for λ3(G) whenever λ3(G) is well-defined. This paper first introduces two combinatorial optimization concepts, that is, maximality and superiority,
of λ3(G), and then proves the Ore type sufficient conditions for G to be maximally and super third edge-connected. These concepts and results are useful in network reliability analysis. |
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| Keywords: | graph third edge-connectivity maximality superiority |
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