连通和

And the formulae for estimatingthe edge-toughness of Cartesian product and Kronecker product of some special graphs are presented.

证明了一类r-正则r=κ′连通非完全图G的边坚韧度近似等于r/21+(1/│V│-1并且提供了估计一些特殊图类的笛卡儿积和Kronecker积的边坚韧度的公式。

Applying the De Caen"s inequality of sum of the squares of the degree and Cauchy"s inequality, we obtain a strict lower bound and a strict upper bound of the largest Laplace eigenvalues only in terms of vertex number of a unicycle graph. Applying the Laplace matrix theorem of trees, we obtain an upper bound of the second smallest Laplace eigenvalues of a unicycle. Extremal graph whose second smallest Laplace eigenvalues reach the obtained upper bound is determined. We also obtain an upper bound of the second largest Laplace eigenvalues in terms of vertex number of the largest connected branch of unicycle graph, and obtain a theoretical method to calculate the second largest Laplace eigenvalues of unicycle graph. We obtain an upper bound of any Laplace eigenvalues in terms of vertex number of a unicycle graph. We also obtain the distribution of Laplace eigenvalues in the inter [0,n] in terms of the matching number.

本文得到了以下几个方面的结果： 1、利用图度平方和的De Caen不等式和Cauchy不等式给出单圈图的最大Laplace特征值仅依赖于顶点数的严格的上下界；利用树的Laplace理论给出了单圈图次小Laplace特征值的一个上界，并刻画了达到该上界的极图；利用子图的连通分支的顶点个数给出了单圈图次大Laplace特征值的一个上界，并给出了单圈图次大Laplace特征值一个理论上的一个求法；利用单圈图的阶数给出了其一般Laplace特征值的一个上界；利用单圈图的匹配数给出其Laplace矩阵谱在区间[0，n]上的分布情况。

In this thesis,we first obtain some sufficient and necessary conditions aboutnormal connected Cayley digraphs,using properties of so called alternating circuit.

本文中，我们首先应用所谓交错回路的性质得到了连通Cayley有向图正规的一些充分的和必要的条件。

In the connected environment it makes more sense to centralize the software and monitor connections in and out.

在连通环境更明智集中监控软件和连接进出。

The "Chunnel", a tunnel connecting England and France, is now complete.

英吉利海峡隧道——一条连通英国和法国的隧道，现在已经完工。（这里complete是形容词，表示"完工的，完成的"。

Some upper and lower bounds of wide diameter of the circulant graphs of degree 4 are also obtained.

根据循环图的传递性和对称性，得到了n阶4度连通循环图的宽直径的上下限。

The heart, blood vessels and lymph vessels connect to form a set of closed pipe system.

心脏、血管和淋巴管互相连通，共同组成一套密闭的管道系统。

Basis on this result, Chen, Lih and Wu put forth the following conjecture:Conjecture 2 For any connected graph G, except K_m, C_(2m+1) and K_(2m+1,2m+1) for all m ≥ 0,then G is equitably △—colorable .

基于这一结果，Chen，Lih和Wu提出了以下猜想：猜想2：如果图G是一个既不是完全图，奇圈又不是完全二部图K_(2m+1，2m+1)，m≥0的连通图，那么G存在均匀Δ-染色。

In Chapter 4, in the above system, the definitions of sensitive dependence on initial value, strong sensitive dependence on initial value and chaos set of a sequence of maps are put forward; Meanwhile, sensitive dependence on initial value of a sequence of maps is promited, and the concept of N - sensitive factor is also proposed; That at the local connected space λ_2/(N-1) is a N—sensitive factor, and a chaotic map containing strong sensitive dependence on initial value of a sequence of maps is proved.

第四章，在上述系统中给出了一列映射的初值敏感依赖、初值强敏感依赖和混沌集的定义；同时又对一列映射的初值敏感依赖进行了推广，提出了该系统下一个N-敏感系数的概念：证明了在局部连通空间中λ_2/N-1是系统的一个N-敏感系数；又证明了一列映射的混沌集蕴涵一列映射对初始条件具有强敏感依赖性。

Introduced a line detection method that is simply connected to the chain, its definition of simple and clear physical significance, easy storage and handling.

采用了一种检测直线的方法，即有向单单连通链法，它定义简单，物理意义明确，易于存储和处理。

By the time of its fall, most of the prisoners were writers who had written against the corruptions of the government.

到它被攻陷的时候，里面多数的犯人是写了反对政府贪污文章的作家。

The most obvious variation to ovum morphological character was that the color was changed from light green to sepiaceous in embryonic development, and all the ovums were almost hatched after 96h.

在胚胎发育过程中卵的形态特征最明显的变化是颜色从淡绿到深褐色，卵在发育96h后卵基本全部孵化。