查询词典 adjacent vertex

The concepts of adjacent vertex distinguishing incidence coloring and the adjacent vertex distinguishing incidence coloring number of graphs are defined on the basis of the concept of incidence coloring of graphs.

在图的关联着色概念的基础上定义了图的邻点可区别关联着色及邻点可区别关联色数，研究了圈、完全二部图、Cm。

In the third chapter, we shall define the concepts of the adjacent vertex distinguishing incidence coloring and the adjacent vertex distinguishing incidence chromatic number of graphs: For graph G, let Q_u={|u"∈N}U{|u∈N},σ: I→C is a k- incidence coloring of graph G, C_u denotes the set of colors assigned to Q_u.

在第三章中我们将定义图的邻点可区别关联着色及邻点可区别关联色数：对图G，设Q_u={|u"∈N}∪{|u∈N}，σ：I→C为图G的k-关联着色，C_u表示着在Q_u上的色集。

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。

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。

If the vertex set of a graph can be partitioned into two disjoint nonempty sets V_(1) and V_(2), every vertex in V_(1) connects every vertex in V_(2) and there is no edge in V_(1) and V_(2), then we call this graph is a complete bipartite graph. If V_(1) contains m elements and V_(2) contains n elements, then we denote this complete bipartite graph K_.

当一个图中的点集合可以分成两个非空的集合V_(1)及V_(2)，若 V_(1)中的每一点都与V_(2)中的点有边相连，且在V_(1)及V_(2)中的点都没有边相连，则称此图为完全二分图；若 V_(1)中有m个点，V_(2)中有n个点，则此完全二分图记为K_。

These are called vertex focal distance because they are measured from the vertex of the lens surface to the lens focal point, The focal powers corresponding to them are the back and front vertex powers.

13从透镜的表面到焦点的距离被称为顶点焦距，是以透镜的前后顶点为起点测量的。与之相对应的屈光度称为前后顶点焦度。

Vertex a is the initial vertex and b is the terminal vertex.

a顶点是始端顶点，而b是末端顶点。

As far as I know, there are two vertex shader assemblers: the Microsoft vertex shader assembler and the NVIDIA vertex and pixel shader macro assembler.

至于我所知道，这有两个顶点着色的汇编程序：Microsof的顶点着色汇编程序及NVIDIA顶点/象素着色宏汇编程序。

A new group of autocorrelation topological index (At、Bt、Ct and Dt) was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. The autocorrelation functions were calculated from the square root of the vertex degree、modified vertex degree and their combination, that is d i、、 and . The matrix description method and the algorithm of computer software have been developed for the new topological index calculation.

针对目前自相关拓扑指数的计算完全依赖于实验参数而存在的问题，以分子拓扑学点价和自相关函数研究为基础，将点价、修正点价及其组合：、、、的平方根分别作为自相关函数中的f，设计开发出一组新的以点价计算为基础的自相关拓扑指数At、Bt、Ct和Dt。

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。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。