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The first part of this text covers the main graph theoretic topics: connectivity, trees, traversability, planarity, colouring, covering, matching, digraphs, networks, matrices of a graph, graph theoretic algorithms, and matroids. These concepts are then applied in the second part to problems in engineering, operations research, and science as well as to an interesting set of miscellaneous problems, thus illustrating their broad applicability. Every effort has been made to present applications that use not merely the notation and terminology of graph theory, but also its actual mathematical results. Some of the applications, such as in molecular evolution, facilities layout, and graffic network design, have never appeared before in book form. Written at an advanced undergraduate to beginning graduate level, this book is suitable for students of mathematics, engineering, operations research, computer science, and physical sciences as well as for researchers and practitioners with an interest in graph theoretic modelling.
Because of its inherent simplicity, graph theory has a wide range of applications in engineering, and in physical sciences. It has of course uses in social sciences, in linguistics and in numerous other areas. In fact, a graph can be used to represent almost any physical situation involving discrete objects and the relationship among them. Now with the solutions to engineering and other problems becoming so complex leading to larger graphs, it is virtually difficult to analyze without the use of computers. This book is recommended in IIT Kharagpur, West Bengal for B.Tech Computer Science, NIT Arunachal Pradesh, NIT Nagaland, NIT Agartala, NIT Silchar, Gauhati University, Dibrugarh University, North Eastern Regional Institute of Management, Assam Engineering College, West Bengal Univerity of Technology (WBUT) for B.Tech, M.Tech Computer Science, University of Burdwan, West Bengal for B.Tech. Computer Science, Jadavpur University, West Bengal for M.Sc. Computer Science, Kalyani College of Engineering, West Bengal for B.Tech. Computer Science. Key Features: This book provides a rigorous yet informal treatment of graph theory with an emphasis on computational aspects of graph theory and graph-theoretic algorithms. Numerous applications to actual engineering problems are incorpo-rated with software design and optimization topics.
Graph theory, being a rigorously investigated field of combinatorial mathematics, is adopted by a wide variety of disciplines addressing a plethora of real-world applications. Advances in graph algorithms and software implementations have made graph theory accessible to a larger community of interest. Ever-increasing interest in machine learning and model deployments for network data demands a coherent selection of topics rewarding a fresh, up-to-date summary of the theory and fruitful applications to probe further. This volume is a small yet unique contribution to graph theory applications and modeling with graphs. The subjects discussed include information hiding using graphs, dynamic graph-based systems to model and control cyber-physical systems, graph reconstruction, average distance neighborhood graphs, and pure and mixed-integer linear programming formulations to cluster networks.
In the spectrum of mathematics, graph theory which studies a mathe matical structure on a set of elements with a binary relation, as a recognized discipline, is a relative newcomer. In recent three decades the exciting and rapidly growing area of the subject abounds with new mathematical devel opments and significant applications to real-world problems. More and more colleges and universities have made it a required course for the senior or the beginning postgraduate students who are majoring in mathematics, computer science, electronics, scientific management and others. This book provides an introduction to graph theory for these students. The richness of theory and the wideness of applications make it impossi ble to include all topics in graph theory in a textbook for one semester. All materials presented in this book, however, I believe, are the most classical, fundamental, interesting and important. The method we deal with the mate rials is to particularly lay stress on digraphs, regarding undirected graphs as their special cases. My own experience from teaching out of the subject more than ten years at University of Science and Technology of China (USTC) shows that this treatment makes hardly the course di:fficult, but much more accords with the essence and the development trend of the subject.
Graph Theory is a branch of discrete mathematics. It has many applications to many different areas of Science and Engineering. This book provides the most up-to-date research findings and applications in Graph Theory. This book focuses on the latest research in Graph Theory. It provides recent findings that are occurring in the field, offers insights on an international and transnational levels, identifies the gaps in the results, and includes forthcoming international studies and research, along with its applications in Networking, Computer Science, Chemistry, and Biological Sciences, etc. The book is written with researchers and post graduate students in mind.
In the world of mathematics and computer science, technological advancements are constantly being researched and applied to ongoing issues. Setbacks in social networking, engineering, and automation are themes that affect everyday life, and researchers have been looking for new techniques in which to solve these challenges. Graph theory is a widely studied topic that is now being applied to real-life problems. The Handbook of Research on Advanced Applications of Graph Theory in Modern Society is an essential reference source that discusses recent developments on graph theory, as well as its representation in social networks, artificial neural networks, and many complex networks. The book aims to study results that are useful in the fields of robotics and machine learning and will examine different engineering issues that are closely related to fuzzy graph theory. Featuring research on topics such as artificial neural systems and robotics, this book is ideally designed for mathematicians, research scholars, practitioners, professionals, engineers, and students seeking an innovative overview of graphic theory.
Graphs can be used to model many types of relations and process dynamics in physical, biological, social and information systems. Many practical problems can be represented by graphs. In this book, the authors present new research on graph theory including the applications of graph theory in architectural analysis; Miesian intersections and comparing and evaluating graph theory approaches to architectural spatial analysis; the algebraic structure of graphs; the combination of graph theory and unsupervised learning applied to social data mining; organising and structuring the contents of mathematical subjects using graph theory; and a modularity-based filtering approach for network immunisation.
Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new bran ches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-tri vially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics. This program, Mathematics and Its Applications, is devoted to such (new) interrelations as exempla gratia: - a central concept which plays an important role in several different mathe matical and/or scientific specialized areas; - new applications of the results and ideas from one area of scientific endeavor into another; - influences which the results, problems and concepts of one field of enquiry have and have had on the development of another.
This book is prepared as a combination of the manuscripts submitted by respected mathematicians and scientists around the world. As an editor, I truly enjoyed reading each manuscript. Not only will the methods and explanations help you to understand more about graph theory, but I also hope you will find it joyful to discover ways that you can apply graph theory in your scientific field. I believe 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. I have to mention that this book assumes the reader to have a basic knowledge about graph theory. The very basics of the theory and terms are not explained at the beginner level. I hope this book will support many applied and research scientists from different scientific fields.