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While typically many approaches have been mainly mathematics focused, graph theory has become a tool used by scientists, researchers, and engineers in using modeling techniques to solve real-world problems.

Graph Theory for Operations Research and Management: Applications in Industrial Engineering presents traditional and contemporary applications of graph theory in the areas of industrial engineering, management science, and applied operations research. This comprehensive collection of research introduces the useful basic concepts of graph theory in real world applications.

This reference presents graph theory concepts with a specific focus on industrial engineering applications. It is intended for readers with industrial engineering backgrounds, including undergraduate and graduate students, researchers, and others in related research areas. The book is divided into two sections: basic concepts and applications. Some specific topics are connectivity, planarity, Hamiltonian paths and cycles, matching theory, digraphs, networks, and adaptive network structures for data/text pattern recognition theory. Chapters begin with a brief abstract and conclude with references and a listing of key terms and definitions. Editors are Farahani (informatics and operations management, Kingston U., UK) and Miandoabchi (researcher, Logistics and Supply Chain Management research group, Iran ministry of industry, mining, and trade).

Nowadays, graph theory is an important analysis tool in mathematics and computer science. Because of the inherent simplicity of graph theory, it can be used to model many different physical and abstract systems such as transportation and communication networks, models for business administration, political science, and psychology and so on.

The purpose of this book is not only to present the latest state and development tendencies of graph theory, but to bring the reader far enough along the way to enable him to embark on the research problems of his own. Taking into account the large amount of knowledge about graph theory and practice presented in the book, it has two major parts: theoretical researches and applications.

Powered by a native graph database, Neo4j stores and manages data in its more natural, connected state, maintaining data relationships that deliver lightning-fast queries, deeper context for analytics, and a pain-free modifiable data model.

This book is prepared as a combination of the manuscripts submitted by respected mathematicians and scientists around the world. As an editor, The author truly enjoyed reading each manuscript. Not only will the methods and explanations help you to understand more about graph theory, but The author also hopes you will find it joyful to discover ways that you can apply graph theory in your scientific field.

The author believes the book can be read from the beginning to the end at once. However, the book can also be used as a reference guide in order to turn back to it when it is needed. The author has to mention that this book assumes the reader to have a basic knowledge about graph theory.

This book aims to explain the basics of graph theory that are needed at an introductory level for students in computer or information sciences. It also aims to provide an introduction to the modern field of network science.

These are introductory lecture notes on graph theory. It offers undergraduates a remarkably student-friendly introduction to graph theory and takes an engaging approach that emphasizes graph theory's history.

This is an introductory book on algorithmic graph theory. Theory and algorithms are illustrated using the Sage open source mathematics software. It's especially suitable for computer scientists and mathematicians interested in computational complexity.

Graph theory might sound like an intimidating and abstract topic to you, so why should you even spend your time reading an article about it? However, although it might not sound very applicable, there are actually an abundance of useful and important applications of graph theory! In this article, I will try to explain briefly what some of these applications are. In doing so, I will do my best to convince you that having at least some basic knowledge of this topic can be useful in solving some interesting problems you might come across.

In this article, I will through a concrete example show how a route planning/optimization task can be formulated and solved using graph theory. More specifically, I will consider a large warehouse consisting of 1000s of different items in various locations/pickup points. The challenge here is, given a list of items, which path should you follow through the warehouse to pickup all items, but at the same time minimize the total distance traveled? For those of you familiar with these kind of problems, this has quite some resemblance to the famous traveling salesman problem. (A well known problem in combinatorial optimization, important in theoretical computer science and operations research).

As you might have realized, the goal of this article is not to give a comprehensive introduction to graph theory (which would be quite a tremendous task). Through a real-world example, I will rather try to convince you that knowing at least some basics of graph theory can prove to be very useful!

I will start with a brief historical introduction to the field of graph theory, and highlight the importance and the wide range of useful applications in many vastly different fields. Following this more general introduction, I will then shift focus to the warehouse optimization example discussed above.

As mentioned previously, I do not aim to give a comprehensive introduction to graph theory. The following section still contains some of the basics when it comes to different kind of graphs etc., which is of relevance to the example we will discuss later on path optimization.

Graph Theory is ultimately the study of relationships. Given a set of nodes & connections, which can abstract anything from city layouts to computer data, graph theory provides a helpful tool to quantify & simplify the many moving parts of dynamic systems. Studying graphs through a framework provides answers to many arrangement, networking, optimization, matching and operational problems.

Just having an abstracted representation of our warehouse in the form of a graph, does of course not solve our actual problem. The idea is rather that through this graph representation, we can now use the mathematical framework and algorithms from graph theory to solve it!

In the end, I hope I have convinced you that graph theory is not just some abstract mathematical concept, but that it actually has many useful and interesting applications! Hopefully, the examples above will be useful for some of you in solving similar problems later, or at least satisfy some of your curiosity when it comes to graph theory and some of its applications.

In this paper we find a particular partition of the vertex set of claw-free strongly chordal graphs in which each element is a clique, and we show that the adjacency graph of these cliques is a tree. In particular, the presented results imply the existence of an ordering of the vertices, and a corresponding edge orientation, such that each directed path is contained in at most two maximal cliques. As shown by the authors in previous works, this allows to give performance guarantee approximation results on a wide class of optimization problems. 2b1af7f3a8