| 图的边韧性度 |
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| 引用本文： | 王志平,任光,赵连昌.图的边韧性度[J].数学研究及应用,2004,24(3):405-410. |
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| 作者姓名： | 王志平 任光 赵连昌 |
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| 作者单位： | 1. 大连海事大学数理系,辽宁,大连,116026
2. 大连海事大学轮机工程学院,辽宁,大连,116026 |
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| 基金项目： | SuppoSed by the Ministry of Communication(200332922505)，the Doctoral Foundation of Ministry of Education(20030151005) |
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| 摘 要： | 文1]中,定义图G(V,E)的边韧性度定义为min{(|S|+T(G-S))/(ω(G-S)):S?E(G)},这里,T-(G-S)和ω(G-S)分别表示G-S中最大分支的顶点数和连通分支数.这是一个能衡量网络图稳定性较好的参数,因为它不仅考虑到了图G-S的分支数也考虑到了它的阶数.在以前的工作中,作者得到了边韧性度图的一个充要条件.利用这些结果证明了K-树是严格边韧性度图,并找到了边韧性度与较高阶的边坚韧度和边坚韧度之间的关系.
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| 关 键 词： | 边割集 严格边韧性度图 K-树 较高阶的边坚韧度 边坚韧度 |
| 收稿时间： | 2002/8/26 0:00:00 |
Edge-Tenacity in Graphs |
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| WANG Zhi-ping,REN Guang and ZHAO Lian-chang.Edge-Tenacity in Graphs[J].Journal of Mathematical Research with Applications,2004,24(3):405-410. |
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| Authors: | WANG Zhi-ping REN Guang and ZHAO Lian-chang |
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| Institution: | Dept. of Math. & Phys.; Dalian Maritime University; Dalian; China;Inst. of Marine Engineering;Dalian Maritime University; Dalian; China;Dept. of Math. & Phys.; Dalian Maritime University; Dalian; China |
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| Abstract: | The edge-tenacity of a graph G(V, E) is defined as min{|S|+τ(G-S)/ω(G-S) : S E(G)},where τ(G-S) and ω(G-S), respectively, denote the order of the largest component and the number of the components of G - S. This is a better parameter to measure the stability of a network G, as it takes into account both the quantity and the order of components of the graph G - S. In a previous work, we established a necessary and sufficient condition for a graph to be edge-tenacious. These results are applied to prove that K-trees are strictly edge-tenacious. A number of results are given on the relation of edge-tenacity and other parameters, such as the higher-order edge toughness and the edge-toughness. |
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| Keywords: | edge cut-sets strictly edge-tenacious graph K-trees higher-order edge toughness edge toughness |
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