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A Beginners Guide To Graph Theory
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Book Synopsis A Beginner's Guide to Graph Theory by : W.D. Wallis
Download or read book A Beginner's Guide to Graph Theory written by W.D. Wallis and published by Springer Science & Business Media. This book was released on 2010-05-05 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concisely written, gentle introduction to graph theory suitable as a textbook or for self-study Graph-theoretic applications from diverse fields (computer science, engineering, chemistry, management science) 2nd ed. includes new chapters on labeling and communications networks and small worlds, as well as expanded beginner's material Many additional changes, improvements, and corrections resulting from classroom use
Book Synopsis A Beginner's Guide to Graph Theory by : W.D. Wallis
Download or read book A Beginner's Guide to Graph Theory written by W.D. Wallis and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because of its wide applicability, graph theory is one of the fast-growing areas of modern mathematics. Graphs arise as mathematical models in areas as diverse as management science, chemistry, resource planning, and computing. Moreover, the theory of graphs provides a spectrum of methods of proof and is a good train ing ground for pure mathematics. Thus, many colleges and universities provide a first course in graph theory that is intended primarily for mathematics majors but accessible to other students at the senior Ievel. This text is intended for such a course. I have presented this course many times. Over the years classes have included mainly mathematics and computer science majors, but there have been several engineers and occasional psychologists as weil. Often undergraduate and graduate students are in the same dass. Many instructors will no doubt find themselves with similar mixed groups. lt is to be expected that anyone enrolling in a senior Ievel mathematics course will be comfortable with mathematical ideas and notation. In particular, I assume the reader is familiar with the basic concepts of set theory, has seen mathematical induction, and has a passing acquaintance with matrices and algebra. However, one cannot assume that the students in a first graph theory course will have a good knowledge of any specific advanced area. My reaction to this is to avoid too many specific prerequisites. The main requirement, namely a little mathematical maturity, may have been acquired in a variety of ways.
Book Synopsis A Beginner's Guide to Graph Theory by : W. D. Wallis
Download or read book A Beginner's Guide to Graph Theory written by W. D. Wallis and published by . This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Beginner’s Guide to Discrete Mathematics by : W.D. Wallis
Download or read book A Beginner’s Guide to Discrete Mathematics written by W.D. Wallis and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to discrete mathematics is aimed at freshmen and sophomores in mathematics and computer science. It begins with a survey of number systems and elementary set theory before moving on to treat data structures, counting, probability, relations and functions, graph theory, matrices, number theory and cryptography. The end of each section contains problem sets with selected solutions, and good examples occur throughout the text.
Book Synopsis Introduction to Graph Theory by : Koh Khee Meng
Download or read book Introduction to Graph Theory written by Koh Khee Meng and published by World Scientific Publishing Company. This book was released on 2007-03-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.
Book Synopsis Expander Families and Cayley Graphs by : Mike Krebs
Download or read book Expander Families and Cayley Graphs written by Mike Krebs and published by OUP USA. This book was released on 2011-10-21 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expander families enjoy a wide range of applications in mathematics and computer science, and their study is a fascinating one in its own right. Expander Families and Cayley Graphs: A Beginner's Guide provides an introduction to the mathematical theory underlying these objects. The central notion in the book is that of expansion, which roughly means the quality of a graph as a communications network. Cayley graphs are certain graphs constructed from groups; they play a prominent role in the study of expander families. The isoperimetric constant, the second largest eigenvalue, the diameter, and the Kazhdan constant are four measures of the expansion quality of a Cayley graph. The book carefully develops these concepts, discussing their relationships to one another and to subgroups and quotients as well as their best-case growth rates. Topics include graph spectra (i.e., eigenvalues); a Cheeger-Buser-type inequality for regular graphs; group quotients and graph coverings; subgroups and Schreier generators; the Alon-Boppana theorem on the second largest eigenvalue of a regular graph; Ramanujan graphs; diameter estimates for Cayley graphs; the zig-zag product and its relation to semidirect products of groups; eigenvalues of Cayley graphs; Paley graphs; and Kazhdan constants. The book was written with undergraduate math majors in mind; indeed, several dozen of them field-tested it. The prerequisites are minimal: one course in linear algebra, and one course in group theory. No background in graph theory or representation theory is assumed; the book develops from scatch the required facts from these fields. The authors include not only overviews and quick capsule summaries of key concepts, but also details of potentially confusing lines of reasoning. The book contains ideas for student research projects (for capstone projects, REUs, etc.), exercises (both easy and hard), and extensive notes with references to the literature.
Download or read book Graph Theory written by Frank Harary and published by . This book was released on 1969 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Beginner’s Guide to Finite Mathematics by : W.D. Wallis
Download or read book A Beginner’s Guide to Finite Mathematics written by W.D. Wallis and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concisely written text in finite mathematics gives a sequential, distinctly applied presentation of topics, employing a pedagogical approach that is ideal for freshmen and sophomores in business, the social sciences, and the liberal arts. The work opens with a brief review of sets and numbers, followed by an introduction to data sets, counting arguments, and the Binomial Theorem, which sets the foundation for elementary probability theory and some basic statistics. Further chapters treat graph theory as it relates to modelling, matrices and vectors, and linear programming. Requiring only two years of high school algebra, this book's many examples and illuminating problem sets - with selected solutions - will appeal to a wide audience of students and teachers.
Book Synopsis A First Course in Graph Theory by : Gary Chartrand
Download or read book A First Course in Graph Theory written by Gary Chartrand and published by Courier Corporation. This book was released on 2013-05-20 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two prominent figures in the field, this comprehensive text provides a remarkably student-friendly approach. Its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.
Book Synopsis The Fascinating World of Graph Theory by : Arthur Benjamin
Download or read book The Fascinating World of Graph Theory written by Arthur Benjamin and published by Princeton University Press. This book was released on 2017-06-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history, formulas, and most famous puzzles of graph theory Graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics—and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond.
Book Synopsis Graphs and Matrices by : Ravindra B. Bapat
Download or read book Graphs and Matrices written by Ravindra B. Bapat and published by Springer. This book was released on 2014-09-19 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.
Book Synopsis A Walk Through Combinatorics by : Miklós Bóna
Download or read book A Walk Through Combinatorics written by Miklós Bóna and published by World Scientific Publishing Company. This book was released on 2011-05-09 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading. The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to [email protected]. Sample Chapter(s) Chapter 1: Seven Is More Than Six. The Pigeon-Hole Principle (181 KB) Chapter 4: No Matter How You Slice It. The Binomial Theorem and Related Identities (228 KB) Chapter 15: Who Knows What It Looks Like,But It Exists. The Probabilistic Method (286 KB) Request Inspection Copy
Download or read book Openscenegraph 3.0 written by Rui Wang and published by Packt Publishing Ltd. This book was released on 2010-12-14 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Create high-performance virtual reality applications with OpenSceneGraph, one of the best 3D graphics engines.
Book Synopsis Graph Representation Learning by : William L. William L. Hamilton
Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
Book Synopsis Monomial Ideals, Computations and Applications by : Anna M. Bigatti
Download or read book Monomial Ideals, Computations and Applications written by Anna M. Bigatti and published by Springer. This book was released on 2013-08-24 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.
Book Synopsis The Practitioner's Guide to Graph Data by : Denise Gosnell
Download or read book The Practitioner's Guide to Graph Data written by Denise Gosnell and published by "O'Reilly Media, Inc.". This book was released on 2020-03-20 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph data closes the gap between the way humans and computers view the world. While computers rely on static rows and columns of data, people navigate and reason about life through relationships. This practical guide demonstrates how graph data brings these two approaches together. By working with concepts from graph theory, database schema, distributed systems, and data analysis, you’ll arrive at a unique intersection known as graph thinking. Authors Denise Koessler Gosnell and Matthias Broecheler show data engineers, data scientists, and data analysts how to solve complex problems with graph databases. You’ll explore templates for building with graph technology, along with examples that demonstrate how teams think about graph data within an application. Build an example application architecture with relational and graph technologies Use graph technology to build a Customer 360 application, the most popular graph data pattern today Dive into hierarchical data and troubleshoot a new paradigm that comes from working with graph data Find paths in graph data and learn why your trust in different paths motivates and informs your preferences Use collaborative filtering to design a Netflix-inspired recommendation system
Book Synopsis Sage Beginner's Guide by : Craig Finch
Download or read book Sage Beginner's Guide written by Craig Finch and published by Packt Publishing Ltd. This book was released on 2011-05-11 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation Your work demands results, and you don't have time for tedious, repetitive mathematical tasks. Sage is a free, open-source software package that automates symbolic and numerical calculations with the power of the Python programming language, so you can focus on the analytical and creative aspects of your work or studies. Sage Beginner's Guide shows you how to do calculations with Sage. Each concept is illustrated with a complete example that you can use as a starting point for your own work. You will learn how to use many of the functions that are built in to Sage, and how to use Python to write sophisticated programs that utilize the power of Sage. This book starts by showing you how to download and install Sage, and introduces the command-line interface and the graphical notebook interface. It also includes an introduction to Python so you can start programming in Sage. Every major concept is illustrated with a practical example. After learning the fundamentals of variables and functions in Sage, you will learn how to symbolically simplify expressions, solve equations, perform integrals and derivatives, and manipulate vectors and matrices. You will learn how Sage can produce numerous kinds of plots and graphics. The book will demonstrate numerical methods in Sage, and explain how to use object-oriented programming to improve your code. Sage Beginner's Guide will give you the tools you need to unlock the full potential of Sage for simplifying and automating mathematical computing. Effectively use Sage to eliminate tedious algebra, speed up numerical calculations, implement algorithms and data structures, and illustrate your work with publication-quality plots and graphics.
