In this paper , the algebraic connectivity of trees is determined by grafting ; meanwhile the relation between the algebraic connectivity and the diameter of two classes of trees is also determined 摘要讨论了树的代数连通度。利用移接变形给出树的代数连通度的一种变化关系，同时给出了两类树的代数连通度与直径的关系。
In the last chapter , we use the results of higher order edge connectivity to study the tree decomposition of transitive graphs , deriving a sufficient condition for a graph to have tree number equivalent to the arboricity 在最后一章中，我们使用高阶边连通度的结果研究对称图中树分解的一个问题，给出了森林数等于树数的一个充分条件。
Particularly , explicit expression for connectivity of cayley digraphs is given , doom and meng ' s results are also generalized and improved . at last , cayley digraphs with optimal connectivity are analyzed 特别地，给出了cayley图连通度的精确表达式，推广并改进了doorn和孟吉祥的结果，并在最后分析了一些达到最优连通度的cayely图类。
All these systems increase their reliability by studying ( among other ) the existence of two ( or more ) disjoint paths connecting any two nodes . to satisfy all these demands , we generalize diameter of graphs to generalized diameter of graphs 这些系统不仅要求我们研究网络的连通度和直径，而且要研究连接两个节点或两个点集间的内部点不交的多条路径。
Graph parameters such as connectivity and diameter have been studied extensively due to their intrinsic importance in graph theory , combinatorics and their relarioiis to ( and applications in ) fault tolerance and transmission delay in communications networks 图的某些参数，如连通度和直径，因为其在图论和组合中固有的重要性及其与通信网络的容错性和传输延迟的关系而得到广泛研究。
Therefore , the pancyclicity is a very important measurement for determining whether a topology of network is suitable for an application , where mapping rings of any length into the topology of network is required 而对于一个网络来说，是否适合于应用，泛圈性是一个重要的决定因素。考察超立方体q _ n和mbius这两个重要的网络拓扑结构，比较他们的泛圈性，连通度等性质，从而比较他们各自的优越性。
Gu to the crossed cube , and proved that for node - to - node routing , the crossed cube can tolerate as many as n - 1 faulty clusters of diameter ai most 1 with at most 2n - 3 ( n > 2 ) faully nodes in total which is as good as the hypercube 交叉立方体的上述这些性质都与超立方体的相同。为了进一步提高连通度，我们改进了交叉立方体的网络拓扑结构，对顶点地址相反的顶点对之间增加一条边，构成加强交叉立方体。
Therefore the research of connectivity and stability of graphs has been a hot point in graph theory for long time . centering on this topic , except connectivity and edge - connectivity in early period , some new connected parameters of graph were introduced in succession 围绕这个问题，除了早期的点(边)连通度外，人们后来又相继引入了一些新的连通性参数，主要有联结数，离散数，完整度和边完整度，粘连度和边粘连度，坚韧度等。
Then , because the connectivity , super connectedness , restricted connectivity and restricted - connectivity of a graph are important parameters to measure fault - tolerance of an interconnection network , they are of very important significance in design and analysis of fault - tolerant interconnection network in reality 图的连通度，超连通度，限制连通度以及限制边连通度是用来测量互连网容错性的重要参数。在实际容错网络设计和分析中有重要意义。
Cycle structure is often used as a connection structure for local area network and as a control and data flow structure for distributed computations in arbitrary networks because of its nice properties such as low connectivity , simplicity , extensibility and its feasible implementation 因为圈结构有一些好的性质如低连通度，简单性，可扩展性，以及它灵活的可实施性，圈结构经常用于作为局域网的连通结构而且用在任意网络中作为可控制的传输数据的结构。
