Algebraic Graph Theory

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Graphs and Matrices

Author : Ravindra B. Bapat
Publisher : Springer
ISBN 13 : 1447165691
Total Pages : 193 pages
Book Rating : 4.4/5 (471 download)

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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.

Algebraic Graph Theory

Author : Chris Godsil
Publisher : Springer Science & Business Media
ISBN 13 : 1461301637
Total Pages : 453 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Algebraic Graph Theory by : Chris Godsil

Download or read book Algebraic Graph Theory written by Chris Godsil and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Graph Theory

Author : Norman Biggs
Publisher : Cambridge University Press
ISBN 13 : 9780521458979
Total Pages : 220 pages
Book Rating : 4.4/5 (589 download)

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Book Synopsis Algebraic Graph Theory by : Norman Biggs

Download or read book Algebraic Graph Theory written by Norman Biggs and published by Cambridge University Press. This book was released on 1993 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a substantial revision of a much-quoted monograph, first published in 1974. The structure is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of 'Additional Results' are included at the end of each chapter, thereby covering most of the major advances in the last twenty years. Professor Biggs' basic aim remains to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first part, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject which has strong links with the 'interaction models' studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with other branches of algebraic combinatorics and group theory. This new and enlarged edition this will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists.

Topics in Algebraic Graph Theory

Author : Lowell W. Beineke
Publisher : Cambridge University Press
ISBN 13 : 9780521801973
Total Pages : 302 pages
Book Rating : 4.8/5 (19 download)

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Book Synopsis Topics in Algebraic Graph Theory by : Lowell W. Beineke

Algebraic Graph Theory

Author : Ulrich Knauer
Publisher : Walter de Gruyter
ISBN 13 : 311025509X
Total Pages : 325 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Algebraic Graph Theory by : Ulrich Knauer

Download or read book Algebraic Graph Theory written by Ulrich Knauer and published by Walter de Gruyter. This book was released on 2011-09-29 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools. They allow to model net structures – like roads, computers, telephones – instances of abstract data structures – like lists, stacks, trees – and functional or object oriented programming. In turn, graphs are models for mathematical objects, like categories and functors. This highly self-contained book about algebraic graph theory is written with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvalues. It ends with a challenging chapter on the topological question of embeddability of Cayley graphs on surfaces.

Isomorphisms, Symmetry and Computations in Algebraic Graph Theory

Author : Gareth A. Jones
Publisher : Springer Nature
ISBN 13 : 3030328082
Total Pages : 234 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Isomorphisms, Symmetry and Computations in Algebraic Graph Theory by : Gareth A. Jones

Download or read book Isomorphisms, Symmetry and Computations in Algebraic Graph Theory written by Gareth A. Jones and published by Springer Nature. This book was released on 2020-01-10 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of a selection of peer-reviewed contributions to the Workshop on Algebraic Graph Theory that took place in Pilsen, Czech Republic in October 2016. Primarily intended for early career researchers, it presents eight self-contained articles on a selection of topics within algebraic combinatorics, ranging from association schemes to symmetries of graphs and isomorphism testing. Algebraic combinatorics is a compelling mathematical discipline based on the powerful interplay of algebraic and combinatorial methods. Algebraic interpretation of combinatorial structures (such as symmetry or regularity) has often led to enlightening discoveries and powerful results, while discrete and combinatorial structures have given rise to new algebraic structures that have found valuable applications. In addition to these original research contributions, the reader will find a survey linking numerous threads in algebraic combinatorics, and an extensive tutorial showcasing the universality of algebraic methods in the study of combinatorial structures.

Fundamentals of Algebraic Graph Transformation

Author : Hartmut Ehrig
Publisher : Springer Science & Business Media
ISBN 13 : 3540311882
Total Pages : 383 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Fundamentals of Algebraic Graph Transformation by : Hartmut Ehrig

Download or read book Fundamentals of Algebraic Graph Transformation written by Hartmut Ehrig and published by Springer Science & Business Media. This book was released on 2006-05-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. It contains an introduction to classical graphs. Basic and advanced results are first shown for an abstract form of replacement systems and are then instantiated to several forms of graph and Petri net transformation systems. The book develops typed attributed graph transformation and contains a practical case study.

Topics in Algebraic Graph Theory

Author : Lowell W. Beineke
Publisher : Cambridge University Press
ISBN 13 : 1107079454
Total Pages : pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Topics in Algebraic Graph Theory by : Lowell W. Beineke

Download or read book Topics in Algebraic Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2004-10-04 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmonic analysis, and are increasingly being used in such areas as computer networks where symmetry is an important feature. Other books cover portions of this material, but this book is unusual in covering both of these aspects and there are no other books with such a wide scope. Peter J. Cameron, internationally recognized for his substantial contributions to the area, served as academic consultant for this volume, and the result is ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory. Each chapter concludes with an extensive list of references.

Modern Graph Theory

Author : Bela Bollobas
Publisher : Springer Science & Business Media
ISBN 13 : 1461206197
Total Pages : 408 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Modern Graph Theory by : Bela Bollobas

Download or read book Modern Graph Theory written by Bela Bollobas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerédis Regularity Lemma and its use, Shelahs extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader.

Graph Algebra

Author : Courtney Brown
Publisher : SAGE
ISBN 13 : 1412941091
Total Pages : 105 pages
Book Rating : 4.4/5 (129 download)

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Book Synopsis Graph Algebra by : Courtney Brown

Download or read book Graph Algebra written by Courtney Brown and published by SAGE. This book was released on 2008 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes an easily applied language of mathematical modeling that uses boxes and arrows to develop very sophisticated, algebraic statements of social and political phenomena.

Algebraic Graph Theory

Author : Ulrich Knauer
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110617366
Total Pages : 349 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Algebraic Graph Theory by : Ulrich Knauer

Download or read book Algebraic Graph Theory written by Ulrich Knauer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-10-08 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph models are extremely useful for a large number of applications as they play an important role as structuring tools. They allow to model net structures – like roads, computers, telephones, social networks – instances of abstract data structures – like lists, stacks, trees – and functional or object oriented programming. The focus of this highly self-contained book is on homomorphisms and endomorphisms, matrices and eigenvalues.

Advanced Graph Theory and Combinatorics

Author : Michel Rigo
Publisher : John Wiley & Sons
ISBN 13 : 1119058643
Total Pages : 290 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Advanced Graph Theory and Combinatorics by : Michel Rigo

Download or read book Advanced Graph Theory and Combinatorics written by Michel Rigo and published by John Wiley & Sons. This book was released on 2016-11-22 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.

Applications of Algebraic Topology

Author : S. Lefschetz
Publisher : Springer Science & Business Media
ISBN 13 : 1468493671
Total Pages : 190 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Applications of Algebraic Topology by : S. Lefschetz

Download or read book Applications of Algebraic Topology written by S. Lefschetz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based, in part, upon lectures given in the Princeton School of Engineering and Applied Science. It presupposes mainly an elementary knowledge of linear algebra and of topology. In topology the limit is dimension two mainly in the latter chapters and questions of topological invariance are carefully avoided. From the technical viewpoint graphs is our only requirement. However, later, questions notably related to Kuratowski's classical theorem have demanded an easily provided treatment of 2-complexes and surfaces. January 1972 Solomon Lefschetz 4 INTRODUCTION The study of electrical networks rests upon preliminary theory of graphs. In the literature this theory has always been dealt with by special ad hoc methods. My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. Part I of this volume covers the following ground: The first two chapters present, mainly in outline, the needed basic elements of linear algebra. In this part duality is dealt with somewhat more extensively. In Chapter III the merest elements of general topology are discussed. Graph theory proper is covered in Chapters IV and v, first structurally and then as algebra. Chapter VI discusses the applications to networks. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.

Spectral Graph Theory

Author : Fan R. K. Chung
Publisher : American Mathematical Soc.
ISBN 13 : 0821803158
Total Pages : 228 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spectral Graph Theory by : Fan R. K. Chung

Download or read book Spectral Graph Theory written by Fan R. K. Chung and published by American Mathematical Soc.. This book was released on 1997 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses spectral graph theory.

Algebraic and Discrete Mathematical Methods for Modern Biology

Author : Raina Robeva
Publisher : Academic Press
ISBN 13 : 0128012714
Total Pages : 382 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Algebraic and Discrete Mathematical Methods for Modern Biology by : Raina Robeva

Download or read book Algebraic and Discrete Mathematical Methods for Modern Biology written by Raina Robeva and published by Academic Press. This book was released on 2015-05-09 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution. Examines significant questions in modern biology and their mathematical treatments Presents important mathematical concepts and tools in the context of essential biology Features material of interest to students in both mathematics and biology Presents chapters in modular format so coverage need not follow the Table of Contents Introduces projects appropriate for undergraduate research Utilizes freely accessible software for visualization, simulation, and analysis in modern biology Requires no calculus as a prerequisite Provides a complete Solutions Manual Features a companion website with supplementary resources

Graph Theory

Author : Bela Bollobas
Publisher : Springer Science & Business Media
ISBN 13 : 1461299675
Total Pages : 191 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Graph Theory by : Bela Bollobas

Download or read book Graph Theory written by Bela Bollobas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject. ... The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and groups. Each chapter starts at a measured and gentle pace. Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text... Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs. Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject. It is this aspect of the book which should guarantee it a permanent place in the literature." #Bulletin of the London Mathematical Society#1

A Brief Introduction to Spectral Graph Theory

Author : Bogdan Nica
Publisher :
ISBN 13 : 9783037191880
Total Pages : 0 pages
Book Rating : 4.1/5 (918 download)

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Book Synopsis A Brief Introduction to Spectral Graph Theory by : Bogdan Nica

Download or read book A Brief Introduction to Spectral Graph Theory written by Bogdan Nica and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Spectral graph theory starts by associating matrices to graphs - notably, the adjacency matrix and the Laplacian matrix. The general theme is then, firstly, to compute or estimate the eigenvalues of such matrices, and secondly, to relate the eigenvalues to structural properties of graphs. As it turns out, the spectral perspective is a powerful tool. Some of its loveliest applications concern facts that are, in principle, purely graph theoretic or combinatorial. This text is an introduction to spectral graph theory, but it could also be seen as an invitation to algebraic graph theory. The first half is devoted to graphs, finite fields, and how they come together. This part provides an appealing motivation and context of the second, spectral, half. The text is enriched by many exercises and their solutions. The target audience are students from the upper undergraduate level onwards. We assume only a familiarity with linear algebra and basic group theory. Graph theory, finite fields, and character theory for abelian groups receive a concise overview and render the text essentially self-contained"--Back cover.