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Autonomous systems of the Internet form a huge complex network connected by physical links,in which the autonomous systems and links among them can be regarded as vertices and edges of an undirected graph.

因特网的自治系统(AutonomousSystem简称AS)构成了一个由物理链路连接起来的庞大的复杂网络,其中的自治系统及其之间的连接可以看作是无向图中的顶点和边。

Broadcast networks can be expressed by a simple connected undirected graph.

将广播网络用简单连通的无向图表示。

In the connected undirected graph with no right to seek a minimum cost spanning tree procedure.

详细说明:在连通的带无权无向图中寻找一个最小代价生成树的程序。

Simulation results demostrate that the circuit simulation algorithmperforms better and it is applicable to more kinds of graphs,such as undirected graphs,directed graphs,and mixed graphs.6 At the end of the article,the applications of the algorithm in several fields aredescribed and the value of the method is pointed out.

测试表明,本算法在对几类常见图的同构判定中表现优于Nauty算法,而且可以适用于无向图、有向图及混合图等多种类型的图。6最后给出了电路模拟法在应用领域的成功应用实例,指出了电路模拟法的应用价值。

Given a ring and a set of communication requests. Each request is represented by a pair of nodes, and associated with a profit. To satisfy a request in the undirected ring, we need to determine a path between the two nodes of the request in the ring. To satisfy a request in the directed ring, we need to determine a directed path from the source to the destination of the request in the directed ring. The goal of the call admission control problem is to determine and satisfy a maximum profit subset of the requests such that for every edge of the ring, the number of satisfied requests that are routed through the edge does not exceed the capacity of the edge.

要在无向环中实现一个呼叫,需在环中指定该请求所对应的两个顶点之间的一条路,要在有向环中实现一个呼叫,需在环中指定该请求的源节点到目的节点的一条路,环网络呼叫接纳控制问题的目标是确定最大利润的呼叫子集,在环中实现该子集中的每一个呼叫,使得经过每一边的呼叫的数目不超过该边的容量,对于无向和有向环网络呼叫接纳控制问题,我们均首次给出了多项式时间近似方案。

Furthermore, we analyze the super restriced edge connectivity for all de Bruijn undirected graphs.

从而全面解决了无向de Bruijn图的超级限制边连通性。

In this thesis, we mainly study the restricted edge connectivity for the de Bruijn digraphs and the super restricted edge connectivity for the de Bruijn undirected graphs.

并介绍了de Bruijn图和限制边连通度方面的基本概念和基本结论。

Unfortunately,all the transitive signature schemes available are undirected ones and can only be used in the case of equivalence relation.

已有的传递签名方案都是无向的,只适用于对等价关系签名,提出有向传递签名方案是个留待解决的公开问题。

During the initial partitioning phase of multilevel method, this paper proposed the algorithm of spectral partitioning for weighted undirected graph and gave the Fiedler vector calculation of Laplacian matrix using the Lanczos iteration method.

在多水平方法初始剖分阶段提出了一种基于谱方法的无向赋权图剖分算法SPWUG,给出了基于Lanczos迭代计算Laplacian矩阵次小特征值及特征向量的实现细节。

In this paper, firstly, not only the incidence matrix ,adjacent matrix, cycle matrix, cut-set matrix of an undirected graph are summarized, but also the close contact between a graph and its corresponding matrix are discussed ; secondly, many problems of a graph which are solved by analysing its matrix are listed as follows:1、The co-tree set of a graph is obtained by using its cycle-matrix ; 2、The branches of its spanning tree are given by using its cut-set matrix ; 3、By making use of the incidence matrix of a graph ,not only its vertex cut 、cut vertex 、isolated point and spanning tree can be obtained ,but also the two sides which are whether parallel or not can be judged ;4、By using their adjacent matrix ,the two graphes which are whether isomorphous or not can be judged; once more, there is a detailed introduction in view of special graph (for example: bigaritite graph ,regular graph and so on);last but not least, a graph method of calculating the N power of a matrix is given and the practical applications of the theorem for degree is indicated.

本文首先综述了无向图的关联矩阵,邻接矩阵,圈矩阵,割集矩阵以及图和它对应矩阵之间的关系;其次总结出了利用上述各类矩阵可以解决的图的若干问题:1、利用图的圈矩阵可以求其连枝集;2、利用图的割集矩阵可以求其生成树的树枝;3、利用图的关联矩阵不仅可以求其割点、点割集、连通度、孤立点和生成树,而且可以判断两条边是否平行;4、利用图的邻接矩阵可以判断两个图是否同构;再次,针对特殊图(例如:二分图、正则图等等)的邻接矩阵作了详细介绍;最后,得到了利用图计算矩阵的N次幂的方法,指出度数定理的实际应用。

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