In 1736, a famous Swiss mathematician Leonhard Euler (1707 – 1783) started the work in the area of Graph Theory through his successful attempt in solving the problem of “Seven Bridges of Konigsberg.” Graph Theory solved many problems in multiple fields (Chinese Postman Problem, DNA fragment assembly, and aircraft scheduling.) In Chemistry, Graph Theory is used in the study of molecules, construction of bonds in chemistry, and the study of atoms. In Biology, Graph Theory is used in the study of breeding patterns or tracking the spread of disease.

Write a three to five (3-5) page paper in which you:

1. Choose two (2) applications for graph theory within your area of specialization (Networking, Security, Databases, Data Mining, Programming, etc.).

2. Examine how these applications are being used in your specialization.

3. Determine how graph theory has advanced the knowledge in your area of specialization.

4. Conclude how you will apply graph theory in your area of specialization.

5. Use at least three (3) quality academic resources in this assignment. Note: Wikipedia and other Websites do not quality as academic resources.

Your assignment must follow these formatting requirements:

· Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides; citations and references must follow APA or school-specific format. In-text citations must be used appropriately and have a corresponding reference entry. Each reference must have at least one in-text citation. Check with your professor for any additional instructions.

· Include a cover page containing the title of the assignment, the student’s name, the professor’s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length.

The specific course learning outcomes associated with this assignment are:

· Model relationships with graphs, functions, and trees.

· Use technology and information resources to research issues in discrete math.

· Write clearly and concisely about discrete math using proper writing mechanics. Applications of Euler’s Graph Theory.

MORE INFO 

Applications of Euler’s Graph Theory

Introduction

Graph theory is the study of graphs and the way they are used in many applications. It is a very important topic, which can be used to solve many mathematical problems. In this article we will discuss some applications of Euler’s graph theory.

Applications of Euler’s Graph Theory

Euler’s graph theory is used in the study of networks and graphs. It is used to describe how two or more objects are connected. Graphs can be used as models for many different situations, including transportation networks, chemical reaction networks, and social network analysis (SNA).

• Transportation Networks: A transportation network is a set of points where each point represents an intersection on the roadways between pairs of cities or towns. The goal of this type of graph is to find out what happens if someone drives from one city to another with no stops along the way?

What is Graph Theory?

Graph theory is a branch of mathematics that deals with graphs and their properties. A graph is a mathematical structure that consists of vertices (the nodes) and edges (the links between two or more vertices). Vertices can be thought of as the dots on the graph, while edges represent the lines connecting them. The following image shows an example:

• Nodes are represented by circles, while edges are represented by lines connecting them together

• Each circle represents one node in our example; each line represents another edge between those two nodes

What is Euler’s Graph Theory?

Euler’s Graph Theory is a branch of mathematics that studies properties of graphs. It was developed by Leonhard Euler, who was one of the most famous mathematicians in history.

Euler’s Graph Theory has applications in different fields such as computer science, engineering and biology.

The Königsberg Bridge Problem

Euler’s graph theory is a way of representing the space of all routes through a network. The Königsberg Bridge Problem is an example of this, where you are given a list of bridges and want to find the route that crosses each bridge exactly once.

This problem has been extensively studied by mathematicians since its first appearance in 1831. It was solved using Euler’s method, which involves finding one or more points at which you can enter any given path into your system and then building up from there until you reach your destination point.

The Bridges of Konigsberg One More Time

So you’ve read the article, and now you’re ready to learn more about Euler’s graph theory. This will be helpful if you want to know how bridges work, or if your friends want to know what a bridge is.

To start with, let’s go back into history. In the year 1736, the famous Königsberg Bridge Problem was posed by Wilhelm von Humboldt (1767-1835). The problem asked: “Are there only seven bridges in this city?” He found that there were indeed only seven bridges spanning across canals within Königsberg, but then he wondered why? And so he went on an expedition through Europe where he collected data about different types of cities—including Paris and London—and compared their structures with each other in order to find out if there were any similarities between them or not.

The Seven Bridges of Königsberg Revisited (Again)

You may have heard of the Seven Bridges of Königsberg, a problem from geometry that has been studied since the 17th century. The problem states that there are seven bridges connected to each other by canals, but only four canals cross at any one time. If you want to get from A to B without crossing any of your friend’s bridges, how many ways can you do it?

The good news is Euler (better known as Leonhard Euler) found an elegant solution in 1736: he used topology! Topology is a branch of mathematics concerned with shape and size in space. Using topological tools like maps/graphs, we can figure out how many paths exist through some region without having to count them up one by one or calculate their length using trigonometry; this saves us time and makes things easier on our brains (and maybe even makes them more fun!).

Other Applications of Euler’s Graph Theory

Euler’s Graph Theory has been used in other areas of mathematics and computer science. In particular, it has been used to solve problems in chemistry. A good example of this is the study of chemical compounds that are formed by reacting two or more substances together. These reactions often produce products that have a long chain structure (e.g., sugars). The structure of these compounds can be described using graphs because they consist of many repeating subunits connected end-to-end with no gap between them. This type of graph was first studied by Euler himself who found out how many possible ways there were for these chains to be arranged on paper or other surfaces such as trees or bushes!

Takeaway:

Euler’s graph theory is a mathematical subject that can be applied in many different ways. It has applications for things like computer science, biology, and more!

The takeaway section is a summary of the article (or chapter) you’re reading. It should be no longer than one or two sentences long and should end with a question mark or exclamation point so that readers know what they’ve just read was important enough to end on.

Conclusion

Euler’s graph theory has been used in a variety of applications, including designing the Königsberg Bridge problem and finding the shortest paths on it. It also played an important role in determining whether or not Fermat’s last theorem was true or false.