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A Halin graph is a plane graph obtained by drawing a tree without vertex of degree 2 in the plane, then drawing a cycle through all leaves in the plane.

Halin图是将一个没有度数为2的点之树画在一平面上，再加上一个通过该树所有叶的圈所得出的平面图。

That means use of three-dimensional CAD Software quickly genera reverse to arrangement stereo line graph of the elbow, then the computer quickly measure out each bus real long, then the method of drawing plane development graph.

该方法主要利用三维CAD软件1：1快速生成弯头的反向排列立体线架图，然后由计算机快速测量出各节的母线实长，进而进行平面展开图绘制。

The classical cutting stock algorithm——column generation technology , and wrap up rectangle technology for abnormity are analyzed ; The development of AutoCAD with ObjectARX is studied and the generating method of cutting outline drawing and layout drawing were found out on the basis of analyses of the graph database structure of AutoCAD and the basic operation of it ; The process planning technology of plate material cutting orienting numerical control is studied a process planning method directly based on layout drawing is established ; The emulation technology in AutoCAD is studied and a kind of dynamic emulation method is put forward , which is realized by incrementally modifying graph entity ; The postposition of NC program of the integrated cutting system constructed on software plug-in is proposed , which can effectively solve the problem that it is difficult for a numerical control programming system to be common , which is caused by the difference of instruction format and control parameter between different type of numerical control machine .

分析了经典的矩形件优化排样算法——列生成法和针对异形件的矩形包络算法；研究了基于ObjectARX 的AutoCAD 开发技术，结合对AutoCAD 图形数据库结构及其基本操作的分析，给出了下料轮廓图和排样图的生成方法；研究了板材数控下料加工的工艺处理技术，建立了一种直接基于排样图进行的图形交互工艺规划方法；研究了在AutoCAD环境中的板材下料数控仿真技术，给出一种通过增量修改图形实体对象实现的动态仿真方法；提出以软插件技术构建集成下料系统的数控编程后置处理部分，能够有效解决因数控下料机床指令格式及控制参数不统一导致的自动编程软件系统不易实现通用性的问题。

This implies the existence of a polynomially bounded algorithm to find a shortest contractible cycle, a shortest separating cycle, and shortest cycle in an embedded graph in the projective plane and answers the open problems raised by Mohar and Thomassen in the case of projective plane embedded graph.

另一方面，通过定义嵌入图的几何对偶图及其相应的嵌入系统，得到几何对偶图中的可分离圈就对应于原图中的割；反之，若几何对偶图中的割在原图中对应于一个圈，那么该圈一定可分离。

In 1987, the well-know mathematician Yousef Alavi and other famous mathematicians defined a new decomposition of graph-Ascending Subgraph Decomposition which is on the condition of proper subgraph isomorphic, and in the same paper they proposed the following ASD conjecture: every graph of positive size has an ASD.

升分解(ascending subgraph decomposition，简记为ASD)是1987年闻名世界的数学家Alavi与其他几位著名数学家给出的一种在真子图同构意义下的图的新分解，并且在同一论文中他们还提出了一个升分解猜想：任意有正数条边的图都可升分解。

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。

Two algorithms, graph cut and random walk based on graph theory, were applied to motion segmentation.

将两种基于图论的算法图切割与随机游走应用于运动对象的分割。

A chart or graph .A line representing data on a graph .

图表上的曲线突降之後逐渐趋於平稳。

Evolution operations on development systems can be naturally expressed by graph rewriting rules. An evolution step is a concrete derivation of a rewriting rule from the graph representing the development system.

在此基础上，我们考察了软件工程中的各种对象在具体图模型上的表示，以及对象间的各种横向和纵向联系。

A line representing data on a graph .The graph flattens out gradually after a steep fall.

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Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。