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Moreover, the smallest degree sum on potentially K(p,1,1)-graphic sequences and k-cycle-graphic sequences are given respectively; bounds on m-restricted edge connectively and 3,4-restricted edge cut of graphs are also characterized respectively.

此外,还分别给出了蕴含k圈和(p,1,1)-部图可图序列度和的下界;分别给出连通图含m-限制边割的充分条件和必要条件及连通度的界。

The connectivity and edge connectivity axe important measure of the network's reliability.

连通度和边连通度是衡量网络可靠性的一个重要参数。

The connectivity and edge connectivity axe important measure of the networks reliability.

连通度和边连通度是衡量网络可靠性的一个重要参数。

In chapter four, we study the second isoperimetric connectivity of line graphs and line digraphs. For line digraphs, we show that the second isoperimetric connectivity of strongly connected line digraphs with δ≥ 2 equals its connectivity. For line graphs, we give a sufficient and necessary condition for the existence of the second isoperimetric connectivity, and we show that under the condition that the second isoperimetric connectivity exists, the second isoperimetric con

第四章研究线图和有向线图的第二等周点连通度,得到了如下结果:(1)最小度大于等于2的强连通有向线图的第二等周点连通度等于它的点连通度;(2)对于无向线图,我们给出了第二等周点连通度存在的充要条件;(3)对于第二等周点连通度存在的无向线图,它的第二等周点连通度或者等于限制点连通度或者等于最小度和次最小度的和。

Let G be a connected graph of order n whose algebraic connectivity, vertex connectivity, and edge connectivity are α,κ, and λ, respectively.

n阶连通图G的代数连通度、点连通度和边连通度分别记作α,κ和λ。

Utilizequadratic form and Perron value of bottleneck matrices, we study how the algebraic connectivityof a weighted tree changes under shifting its branches and changing its edge s weights and obtainmore entire information about algebrai.

利用代数连通度的二次型形式和瓶颈矩阵的Perron值,我们研究了当迁移或改变分支和变动一些边的权重时树的代数连通度的变化,得到了比过去更多的关于赋权树的代数连通度的结论。

In fact, on one hand, it is often found that two graphs with the same number of verticesand the same connectivity(edge-connectivity) may result in entirely different forms after a minimum disconnecting set of vertices is removed, one may be totally disconnected while the other may consist of a few very stable components, and thus be much easier to reconstruct.On the other hand, we often face this question: how easily can we disrupt a system at the least cost, on the contrary, when we set up a system, especially a communication system, we try our best to make it as stable as possible that it can be reconstructed easily if it do get disrupted .

对于两个具有相同点数,具有相同点连通度的图,从图中分别去掉使图不连通的点集后,所得图的结构可能完全不同,这是因为点连通度、边连通度和局部点、边连通度等连通性参数仅反映了系统被破坏的难易程度,而对系统遭受破坏的程度并没有明确的反映。

The minimum number of verticesof G whose removal from G results either in a graph that is no longer connected or in a trivial graph with a single vertex: at least K vertices must be removed from a graph with K-connectivity.

从图g中移去顶点使图成为一个非连通图或是单个顶点的"平凡图"的最少顶点数称为连通度。一个k连通度的图至少必须从图g中移去k个顶点才能成为非连通图。

The procedure of the analysis is as follows :first,the digital road map was made based on the paper map ofFangshan,southwest Beijing,andthefire distribution map was made byinputingthefire points collected withGPSinto the GIS.The road connectivity was obtained using the Axwoman to drawlines along the roads.Buffers onthe lines within a distance of 1 000m were made,and the curver fitting was analyzed between the fire numbers and the road connectivity.

首先对房山区的纸质地形图进行扫描,制作房山的道路分布专题图,并将GPS采集的林火火点位置转入ArcView GIS,制作林火火点位置图;用Axwoman扩展模块勾绘了道路,进行了道路连通度的分析,并以勾绘的连通线作了1 000 m的缓冲分析;以连通度与相应的缓冲区内的林火火点数作了拟合分析。

In the project, we found a method for designing a family of 4-optimal double loop networks, established some sharp upper bounds of forwarding indices, distance domination nember, the edge-connectivity and the sharp upper bounds of wide-diameter and fault-tolerant diameter of Cartesian product graphs, the lower bounds of restricted edge-connectivity of digraphs and a sufficient and necessary condition for the restricted edge-connectivity of a graph to be equal to the restricted connectivity of its line graphs; raveled pancyclicity and panconnectivity and obtained the exact values of the mentioned parameters for some well-known networks.

本项目给出最优双环网络的设计方法,找到4紧优双环网络无限族,建立了路由转发指数紧的界,确定了笛卡尔乘积图的边连通度的表达式,宽直径和容错直径紧的上界,给出有向图限制边连通度的下界和无向图的限制边连通度等于它的线图限制点连通度的充要条件,对一些著名的网络确定了上述参数的精确值,讨论了宽直径和容错直径之间的关系,解决了超立方体某些变型网络的泛圈性和泛连通性,得到距离控制数的紧的上界。

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