# 数学代写|图论作业代写Graph Theory代考|MATH3V03

#### Doug I. Jones

Lorem ipsum dolor sit amet, cons the all tetur adiscing elit

couryes-lab™ 为您的留学生涯保驾护航 在代写图论Graph Theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写图论Graph Theory代写方面经验极为丰富，各种代写图论Graph Theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
couryes™为您提供可以保分的包课服务

## 数学代写|图论作业代写Graph Theory代考|Eulerian Graphs

Looking back at the Königsberg Bridge Problem, we now have the necessary pieces to describe the question in graph theoretic terminology, namely an exhaustive circuit that includes all vertices and edges of the graph. In honor of Euler’s solution, these special types of circuits bear his name.

Definition 2.6 Let $G$ be a graph. An eulerian circuit (or trail) is a circuit (or trail) that contains every edge and every vertex of $G$.

If $G$ contains an eulerian circuit it is called eulerian and if $G$ contains an eulerian trail but not an eulerian circuit it is called semi-eulerian.
Part of Euler’s brilliance was not only his ability to quickly solve a puzzle, such as the Königsberg Bridge Problem, but also the foresight to expand on that puzzle. What makes a graph eulerian? Under what conditions will a city have the proper tour? In his original paper, Euler laid out the conditions for such a solution, though as was typical of the time, he only proved a portion of the statement (see [6] or $[33]$ ).

The theorem above is of a special type in mathematics. It is written as an “if and only if” statement, which indicates that the conditions laid out are both necessary and sufficient. A necessary condition is a property that must be achieved in order for a solution to be possible and a sufficient condition is a property that guarantees the existence of a solution.

For a more familiar example, consider renting and driving a car. If you want to rent a car, a necessary condition would be having a driver’s license; but this condition may not be sufficient since some companies will only rent a car to a person of at least 25 years of age. In contrast, having a driver’s license is sufficient to be able to drive a car, but is not necessary since you can drive a car with a learner’s permit as long as a guardian is present.

Mathematicians often search for a property (or collection of properties) that is both necessary and sufficient (such as a number is even if and only if it is divisible by 2). The theorem above gives both necessary and sufficient conditions for a graph to be eulerian. It should be clear why connectedness must be achieved if every vertex is to be reached in a single tour. Can you explain the degree condition? When traveling through a graph, we need to pair each entry edge with an exit edge.

## 数学代写|图论作业代写Graph Theory代考|Algorithms

As we now know when a graph will be eulerian or semi-eulerian, the next obvious question is how do we find one. There are numerous methods for finding an eulerian circuit (or trail), though we will focus on only two of these. Each of these algorithms will be described in terms of the input, steps to perform, and output, so it is clear how to apply the algorithm in various scenarios. See Appendix E for the pseudocode for various algorithms appearing in this book. For more a more technical discussion of the algorithms, the reader is encouraged to explore [8] or [52].

The first method for finding an eulerian circuit that we discuss is Fleury’s Algorithm. Although Fleury’s solution was not the first in print, it is one of the easiest to walk through (no pun intended) [35]. As with all future algorithms presented in this book, an example will immediately follow the description of the algorithm and further examples are available in the Exercises. Note that Fleury’s Algorithm will produce either an eulerian circuit or an eulerian trail depending on which solution is possible.

The intention behind Fleury’s Algorithm is that you are prevented from getting stuck at a vertex with no edges left to travel. In practice, it may be helpful to use two copies of the graph-one to keep track of the route and the other where labeled edges are removed. This second copy makes it easier to see which edges are unavailable to be chosen. In the example below, the vertex under consideration during a step of the algorithm will be highlighted and edges will be labeled in the order in which they are chosen.

# 图论代考

## 数学代写|图论作业代写Graph Theory代考|Algorithms

Fleury 算法背后的意图是防止您卡在一个没有边可以移动的顶点。在实践中，使用图形的两个副本可能会有所帮助 – 一个用于跟踪路线，另一个用于删除标记的边缘。这第二个副本可以更容易地看到哪些边缘不可用以供选择。在下面的示例中，算法步骤中考虑的顶点将突出显示，边将按照选择它们的顺序进行标记。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

Days
Hours
Minutes
Seconds

# 15% OFF

## On All Tickets

Don’t hesitate and buy tickets today – All tickets are at a special price until 15.08.2021. Hope to see you there :)