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# 数学代写|图论代考GRAPH THEORY代写|Lights Out

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## 数学代写|图论代写GRAPH THEORY代考|Lights Out

On a certain floor of a business building, a firm occupies three offices A, B and C located in a row. Each office has a large ceiling light and a light button which, when pressed, reverses the light in that office (on to off or off to on) as well as the light in each adjacent office. So if we begin the day, as in Figure 13.20(a), with all lights off and push the light button in the central office B, then we arrive at the situation in Figure 13.20(b), where all lights are on.

Each light arrangement of the three offices can be represented by an ordered triple $(a, b, c)$ or $a b c$, where $a, b$ and $c$ can be 0 or 1 , with 0 meaning that the light is off in the particular office and 1 meaning that the light is on. The eight possibilities are shown in Figure 13.21.

This situation can be represented by a graph $G$ of order 8 , whose vertices are the ordered triples $a b c$, where $a, b, c \in{0,1}$. If we can change from one light arrangement to another by pressing a single light button, then we draw an edge between the two vertices representing these arrangements. The graph $G$ is shown in Figure 13.22. You might notice that $G$ is the 3-cube $Q_3$. The graph $Q_3$ of Figure 13.22 shows that, beginning with lights out in all three offices, we can obtain any light pattern we desire, although it may require pressing as many as three buttons.

## 数学代写|图论代写GRAPH THEORY代考|And Still It Grows More Colorful

We have seen that graph theory originated with a number of isolated and disconnected results from unexpected sources. Recreational results and truly mathematical theorems alike played major roles in
the development of the subject. Authors of the early textbooks on graph theory organized many of the existing theorems and set the stage for what was to follow. Progress in graph theory was greatly aided by numerous attempts to solve a simple-sounding but deceptively difficult problem involving the coloring of maps. Graph theory had the good fortune, however, of attracting a number of talented and dedicated mathematicians to this fascinating subject.

As graph theory progressed further into the 20th century, some well-defined areas of the subject blossomed. Also, the number of mathematicians working in the subject continued to grow. This included researchers who obtained deep results, those who studied graph theory from applied points of view, those who created new and interesting problems to study, those who wrote of the historical perspectives of the subject and its relationships to other more established areas of mathematics and those who wrote and lectured of the many aesthetic aspects of the subject, thereby introducing graph theory to a new generation of mathematicians. That graph theory had grown into a more prominent area of mathematics became increasingly evident during the latter portion of the 20th century and into the 21 st century.

In the 1960s a series of conferences that emphasized graph theory came into prominence. One of these was the 1963 Czechoslovak Symposium on Graph Theory held in Smolenice. In 1968 the first of nine Kalamazoo (Michigan) Graph Theory Conferences was held and would continue to take place every fourth year at Western Michigan University throughout the remainder of the 20th century. Yousef Alavi played a leading role in organizing these conferences. In 1969 the first of the Southeastern International Conferences on Combinatorics, Graph Theory and Computing, primarily at Florida Atlantic University and organized by Frederick Hoffman. The British Combinatorial Conferences also began in 1969 and have been held during odd-numbered years since 1973. In more recent times, during even-numbered years, the SIAM (Society for Industrial and Applied Mathematics) Conferences on Discrete Mathematics have taken place.

## 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。