| 图的孤立断裂度 |
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| 引用本文： | 王世英,杨玉星,林上为,李晶,胡志明.图的孤立断裂度[J].数学学报,2011(5):861-874. |
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| 作者姓名： | 王世英 杨玉星 林上为 李晶 胡志明 |
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| 作者单位： | 山西大学数学科学学院;山西大学计算机与信息技术学院; |
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| 基金项目： | 国家自然科学基金资助项目(61070229) |
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| 摘 要： | 连通图G的孤立断裂度isc(G)=max{i(G-S)-|S|:S∈C(G)},其中i(G-S)是G-S中的孤立点数,C(G)是G的点割集.本文研究了孤立断裂度和图的其它一些参数的关系.讨论了孤立断裂度取特殊值的一些图,证明了圈、连通二部图、连通二部图的联图以及树和圈的补图的孤立断裂度都达到最小.给出了具有给定阶数和最大度的村的最大、最小孤立断裂度.
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| 关 键 词： | 网络 可靠性 孤立断裂度 |
The Isolated Scattering Number of Graphs |
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| Shi Ying WANG School of Mathematical Science,Shanxi University,Taiyuan,P.R.China Yu Xing YANG School of Computer Science , Technology,Taiyuan ,P.R.China Shang Wei LIN Jing LI Zhi Ming HU School of Mathematical Science,P.R.China.The Isolated Scattering Number of Graphs[J].Acta Mathematica Sinica,2011(5):861-874. |
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| Authors: | Shi Ying WANG School of Mathematical Science Shanxi University Taiyuan PRChina Yu Xing YANG School of Computer Science Technology Taiyuan PRChina Shang Wei LIN Jing LI Zhi Ming HU School of Mathematical Science PRChina |
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| Institution: | Shi Ying WANG School of Mathematical Science,Shanxi University,Taiyuan,030006,P.R.China Yu Xing YANG School of Computer Science and Technology,Taiyuan 030006,P.R.China Shang Wei LIN Jing LI Zhi Ming HU School of Mathematical Science,P.R.China |
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| Abstract: | The isolated scattering number isc(G) = max{i(G—S)—|S|:S∈C(G)}, where G is a connected graph,i(G - S) is the number of isolated vertices of G - S and C(G) is the set of vertex cuts of G.In this paper,we investigate the relationships between the isolated scattering number and other parameters of a graph G,and discuss the graphs with special isolated scattering numbers.We prove that the isolated scattering numbers of a cycle,a connected bipartite graph,the join of connected bipartite graphs and the complement of a tree and a cycle are minimal,and give the maximum and minimum isolated scattering numbers of trees with given order and maximum degree. |
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| Keywords: | networks vulnerability isolated scattering number |
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