查询词典 planar graph

The dissertation details the functions and characteristic of curves graph element, polygon graph element, character graph element, dimension graph element, parameter graph element, self-define graph element, and research comprehensively the methods describe and graph element attrib. After discussing the basic graph element collection, this thesis gives the description method, organization way, graph element visitation, save and load efficiency, suitability and so on of every element in the basic graph element collection in greater detail. The author provides a graph element data structure organized version which is length changeable and is a block storage record, and designs a new module of data, which can process both the geometry attrib and no geometry attrib of drawing element. Based on this, the data model of all kind of element is put forward.

对采矿CAD系统中基本图元集的构造原则和组织方法进行了研究，提出了一个7元素采矿CAD基本图元集构造方案；论文详细讨论了曲线图元、字符图元、尺寸标注图元、多边形图元、参数图元、自定义图元在采矿CAD系统中的作用和特点，并对各种图元的表述方法和图元属性及相应的库组织方式、存取效率进行了深入的研究，提出了一个&可变长记录块&图元库结构组织方案；通过对采矿CAD系统中基本图元数据模型的构造方法、存取结构和访问方式的研究，给出了一个用C++语言描述的采矿CAD系统基本图元数据模型及其数据存取结构。

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。

Then we prove the one-to-one corresponding relation between 3-coloring of inducing four regular graph and 4-coloring of maximal planar graph and find out the relation between three colors of inducing four regular graph and three dual bi-chromatic subgraph of maximal planar graph.

本文给出了极大平面图的导出四正则图的两种构造方式、等价性及性质，证明了导出四正则图的三着色与原极大平面图四着色的一一对应关系，并且找出了导出四正则图的三种颜色与原极大平面图四着色的三组对偶二色子图之间的关系。

In the special case when G = AutX, we call a G—vertex-transtive graph, G—edge-transtive graph, G—semisymmetric graph X is vertex-transtive edge-transtive semisymmetric graph respectively In this paper we investigate the autmorphism graph AutX of the cubic semisymmetric graph of order 12p ,when p is primes.

特别地，若G=AutX这时的G-点传递图、G-边传递图、G-半对称图称为点传递图边传递图半对称图。

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。

Graph theory s 02 graph theory widely used for its own development. 40-60 20th century era matroid theory and graph theory-very graph theory, algebra and graph theory. topology theory has great development.

详细说明：图论讲义02 图论的广泛应用，促进了它自身的发展。20世纪40-60年代，拟阵理论、超图理论、极图理论，以及代数图论、拓扑图论等都有很大的发展。

Moreover, the range of m is obtained when G is a forest, a unicyclic graph, a bicyclic graph, a tricyclic graph and a tetracyclic graph, respectively, and the graph is determined when m(≥1) takes different value in its range.

给出了当G是森林、单圈图、双圈图、三圈图、四圈图时m的取值范围，并确定了m(≥1)在该取值范围内取不同值时的所有图。

In Chapter 2,we prove that:(1)each planar graph without {4,6,7,9}-cycles is 3-colorable;(2)each planar graph without {4,6,8}-cycles is 3-colorable.

在第二章中，我们证明了以下两个结果：(1)每个不包含{4，6，7，9}-圈的平面图是3-可染色的；(2)每个不包含{4，6，8}-圈的平面图是3-可染色的。

We therefore sometimes refer to a planar embedding of a planar graph as a plane graph.

一个平图G把平面划分成若干个连通区域，这些区域的闭包称为G的面。

In Chapter 3,we obtain that:(1)each planar graph without 4-cycles is acyclically 6-choosable;(2)each planar graph without 4-cycles and without triangles at dis-tance less than 3 is acyclically 5-choosable.

在第三章中，我们获得了以下两个结果：(1)每个不包含4-圈的平面图是无圈6-可选择的；(2)每个不包含4-圈并且任意两个三角形之间的距离至少是3的平面图是无圈5-可选择的。

The circulation, consumption and reproduction of the trilogy have not only testified to its historical significance and literariness, but also invested it with new meanings.

该三部曲的流通、消费与再生产不仅验证了其历史意义及文学性，而切还赋予它以新的意义。

If he thought that he could buy me off, he would be wrong.

如果他认为他可以收买我，那他就大错特错了。