正则图

We shall use algebraic methods to study graphs which are highly regular although this regularity is not expressed in terms of the automorphism group.

我们将用代数方法来研究高度正则的图，尽管这种正则性不是用自同构群来表达的。

Let G be a finite group, and S a subset of G not containing theidentity element 1. The Cayley digraph Cay on G with respect to S is definedas a directed graph with vertex set G and edge set {|g∈G, s∈S}. IfS~(-1)=S, then Cay is undirected and in this case, we view two directededges and as an undirected edge {u, v}. Obviously, the right regularrepresentation R of G, the acting group of G by right multiplication, is asubgroup of the full automorphism group AutCay(G, S of Cay.

给定有限群G，设S是G的不含单位元1的子集，群G关于子集S的Cayley有向图Cay是一个以G顶点集合，而以｛|g∈G，s∈S｝为边集合的有向图，特别地，若S~(-1)=S，则X=Cay是无向的，此时我们把一条无向边｛u，v｝等同于两条有向边和，易见，群G的右正则表示R，即G在G上的右乘作用，为图Cay的全自同构群AutCay

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。

In particular, Neumaier asserted that the collinearity graph of a unique 3/2-design if it meets some constraints over its parameters.

Neumaier在1976年的论文提到，若强正则重边图的参数满足某些条件，这个强正则重边图就会是唯一的3/2-设计的共线性图。

The use of regularization method for the restoration of blurred images of the algorithm, resulting in an image, and then adding noise to the input of specific parameters of regularization to restore its image.

详细说明：利用正则化方法对模糊图像进行恢复的算法，产生一幅图象，然后加入噪声后对特定的输入正则化参数其进行图象恢复。

It is known that with the development of graph theory in the mathematical field, the research value of Hamilton-graphs in graph theory is much more protuberant than before.

此外，本文还研究了在小阶图中是否存在3-正则4-可序哈密尔顿图的问题。

Let G be a k-regular connected vertex transitive graph.

设图G是一个κ-正则连通点可迁图。

This observation strenghen to some extent the corresponding result obtained by Watkins, which said that k-regular vertex transitive graph G has a factor with components isomorphic to a vertex transitive graphs if G is not k connected.

此结果在某种程度上加强了Watkins的相应命题：如果κ正则点可迁图G不是κ连通的，那么G有一个因子，它的每一个分支都同构于同一个点可迁图。

In chapter 4, we studythe cyclic edge connectedness of regular half vertex transitive graphs, we showthat a connected k(≥4)-regular half vertex transitive graph X with girthg≥6 isλ_c-optimal, and we also obtain a su?cient and necessary conditionfor a connected k(≥4)-regular half vertex transitive graph X with girth 4 tobeλ_c-optimal.

第四章，我们研究了正则半点传递图的圈边连通性问题，主要结果是证明了一个围长为g≥6的k(≥4)-正则连通半点传递图X是λ_c-最优的，并且得到了一个围长为g = 4的k(≥4)-正则连通半点传递图X是λ_c-最优的充分必要条件。

Some necessary conditions are obtained for sequential graphs, regular sequential graphs and Euler sequential graphs; several non-sequential graphs classes are showed for conglutinating graphs. The sequential graphs that contain even cycle with the same vertices have been constructed.

使用这种方法，得到了一般序列图、正则序列图、Euler序列图、圈的粘接序列图和圈的并序列图的必要条件，证明了边数为2k， k是奇数的Euler图是非序列图类，讨论了m个n圈的粘接图中的非序列图类；分析偶圈的特征，构造了偶圈的具有同顶点集的序列母图井给出其序列标号表达式。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。