19th Ave New York, NY 95822, USA

# 数学代写|图论代写Graph Theory代考|Drawing graphs

my-assignmentexpert™ 图论代写Graph Theory作业代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。my-assignmentexpert™， 最高质量的图论代写Graph Theory作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此图论代写Graph Theory作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

my-assignmentexpert™ 为您的留学生涯保驾护航 在数学Mathematics作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的数学Mathematics代写服务。我们的专家在图论代写Graph Theory代写方面经验极为丰富，各种图论代写Graph Theory相关的作业也就用不着 说。

## 数学代写|图论代写Graph Theory代考|Graph embeddings

To illustrate why properly drawing graphs may be important, consider the graphs from Figure 2.14, which shows the Petersen graph, a particular $3-$ regular graph. Clearly, by just looking at these drawings, it is not obvious that we are dealing with the same graph (i.e., same in the sense of isomorphic). This instantly brings up the issue of what makes a good drawing of a graph. In this example, either Figure $2.14(\mathrm{a})$ or (b) is arguably the best one.
Formally, when drawing graphs we are considering so-called graph embeddings: a representation of a graph on a surface where vertices are associated with points on that surface. In practice, we always consider the two-dimensional plane, but note that embeddings in three dimensions are also possible.

## 数学代写|图论代写Graph Theory代考|Planar graphs

Let us now take a look at an important class of graphs where topology plays a role, namely graphs that can be drawn in such a way that no edges cross each other, so-called planar graphs.

Definition 2.15: A plane graph is a specific embedding of a graph $G$ such that no two edges intersect. If such an embedding exists, $G$ is said to be planar.

It is not difficult to see why planarity can play an important role. Consider, for example, designing a transportation network. If the corresponding graph is planar, this means that there is no need for multi-layer crossings such as bridges and tunnels. As another example, consider the design of electrical circuits, such as those for chips. In this case, it is important that the wires that connect components do not cross each other. Unfortunately, designing modern chips under the constraint that the associated graph must be planar is very difficult, if not impossible. The alternative, is to design chips as a collection of layers, each layer having an associated planar graph. We will later discuss another intriguing application of planar graphs, namely the coloring of maps. Before doing so, we first consider a number of characteristic properties of planar graphs.

When considering a plane graph, we will observe a number of regions (also called faces), which are enclosed by the edges of the graph. For example, Figure $2.18$ shows a graph with 12 regions. Each region, except $r_{1}$, is enclosed by a cycle. Region $r_{1}$ is referred to as an exterior region; the others are interior regions.

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。