Applied Graph Theory An Introduction With Graph Optimization And Algebraic Graph Theory
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Author | : Christopher H Griffin |
Publisher | : World Scientific |
Total Pages | : 305 |
Release | : 2023-08-08 |
Genre | : Mathematics |
ISBN | : 981127312X |
This book serves as an introduction to graph theory and its applications. It is intended for a senior undergraduate course in graph theory but is also appropriate for beginning graduate students in science or engineering. The book presents a rigorous (proof-based) introduction to graph theory while also discussing applications of the results for solving real-world problems of interest. The book is divided into four parts. Part 1 covers the combinatorial aspects of graph theory including a discussion of common vocabulary, a discussion of vertex and edge cuts, Eulerian tours, Hamiltonian paths and a characterization of trees. This leads to Part 2, which discusses common combinatorial optimization problems. Spanning trees, shortest path problems and matroids are all discussed, as are maximum flow problems. Part 2 ends with a discussion of graph coloring and a proof of the NP-completeness of the coloring problem. Part 3 introduces the reader to algebraic graph theory, and focuses on Markov chains, centrality computation (e.g., eigenvector centrality and page rank), as well as spectral graph clustering and the graph Laplacian. Part 4 contains additional material on linear programming, which is used to provide an alternative analysis of the maximum flow problem. Two appendices containing prerequisite material on linear algebra and probability theory are also provided.
Author | : Chris Godsil |
Publisher | : Springer Science & Business Media |
Total Pages | : 453 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461301637 |
This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.
Author | : Christopher Griffin |
Publisher | : World Scientific Publishing Company |
Total Pages | : 0 |
Release | : 2023-08 |
Genre | : Graph theory |
ISBN | : 9789811273100 |
This book serves as an introduction to graph theory and its applications. It is intended for a senior undergraduate course in graph theory but is also appropriate for beginning graduate students in science or engineering. The book presents a rigorous (proof-based) introduction to graph theory while also discussing applications of the results for solving real-world problems of interest. The book is divided into four parts. Part 1 covers the combinatorial aspects of graph theory including a discussion of common vocabulary, a discussion of vertex and edge cuts, Eulerian tours, Hamiltonian paths and a characterization of trees. This leads to Part 2, which discusses common combinatorial optimization problems. Spanning trees, shortest path problems and matroids are all discussed, as are maximum flow problems. Part 2 ends with a discussion of graph coloring and a proof of the NP-completeness of the coloring problem. Part 3 introduces the reader to algebraic graph theory, and focuses on Markov chains, centrality computation (e.g., eigenvector centrality and page rank), as well as spectral graph clustering and the graph Laplacian. Part 4 contains additional material on linear programming, which is used to provide an alternative analysis of the maximum flow problem. Two appendices containing prerequisite material on linear algebra and probability theory are also provided.
Author | : John Adrian Bondy |
Publisher | : London : Macmillan Press |
Total Pages | : 290 |
Release | : 1976 |
Genre | : Mathematics |
ISBN | : |
Author | : David Avis |
Publisher | : Springer Science & Business Media |
Total Pages | : 273 |
Release | : 2005-12-06 |
Genre | : Business & Economics |
ISBN | : 0387255923 |
Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem. Graph Theory and Combinatorial Optimization explores the field's classical foundations and its developing theories, ideas and applications to new problems. The book examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application. The field's leading researchers have contributed chapters in their areas of expertise.
Author | : Junming Xu |
Publisher | : Springer Science & Business Media |
Total Pages | : 343 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 1441986987 |
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.
Author | : Dieter Jungnickel |
Publisher | : Springer Science & Business Media |
Total Pages | : 597 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662038226 |
Revised throughout Includes new chapters on the network simplex algorithm and a section on the five color theorem Recent developments are discussed
Author | : Jeremy Kepner |
Publisher | : SIAM |
Total Pages | : 388 |
Release | : 2011-01-01 |
Genre | : Mathematics |
ISBN | : 9780898719918 |
The current exponential growth in graph data has forced a shift to parallel computing for executing graph algorithms. Implementing parallel graph algorithms and achieving good parallel performance have proven difficult. This book addresses these challenges by exploiting the well-known duality between a canonical representation of graphs as abstract collections of vertices and edges and a sparse adjacency matrix representation. This linear algebraic approach is widely accessible to scientists and engineers who may not be formally trained in computer science. The authors show how to leverage existing parallel matrix computation techniques and the large amount of software infrastructure that exists for these computations to implement efficient and scalable parallel graph algorithms. The benefits of this approach are reduced algorithmic complexity, ease of implementation, and improved performance.
Author | : Adrian Bondy |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2010-10-19 |
Genre | : Mathematics |
ISBN | : 9781849966900 |
The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated. The book also serves as an introduction to research in graph theory.
Author | : Terry A. McKee |
Publisher | : SIAM |
Total Pages | : 213 |
Release | : 1999-01-01 |
Genre | : Mathematics |
ISBN | : 9780898719802 |
Finally there is a book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics.