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 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no other book with such a wide scope of both areas of algebraic graph theory.
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.
Download or read book Topics in Algebraic Graph Theory written by Lowell W. Beineke and published by . This book was released on 2014-05-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no other book with such a wide scope of both areas of algebraic graph theory.
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 197 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.
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.
Download or read book Topics in Structural Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2012-11-08 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapidly expanding area of structural graph theory uses ideas of connectivity to explore various aspects of graph theory and vice versa. It has links with other areas of mathematics, such as design theory and is increasingly used in such areas as computer networks where connectivity algorithms are an important feature. Although other books cover parts of this material, none has a similarly wide scope. Ortrud R. Oellermann (Winnipeg), internationally recognised for her substantial contributions to structural graph theory, acted as academic consultant for this volume, helping shape its coverage of key topics. The result is a collection of thirteen expository chapters, each written by acknowledged experts. These contributions have been carefully edited to enhance readability and to standardise the chapter structure, terminology and notation throughout. An introductory chapter details the background material in graph theory and network flows and each chapter concludes with an extensive list of references.
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.
Download or read book Algebraic Combinatorics written by Richard P. Stanley and published by Springer Science & Business Media. This book was released on 2013-06-17 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
Download or read book Topics in Graph Theory written by Jonathan L Gross and published by CRC Press. This book was released on 2023-05-24 with total page 904 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay continues to grow between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences. Topics in Graph Theory is geared toward the more mathematically mature student. The first three chapters provide the basic definitions and theorems of graph theory and the remaining chapters introduce a variety of topics and directions for research. These topics draw on numerous areas of theoretical and applied mathematics, including combinatorics, probability, linear algebra, group theory, topology, operations research, and computer science. This makes the book appropriate for a first course at the graduate level or as a second course at the undergraduate level. The authors build upon material previously published in Graph Theory and Its Applications, Third Edition, by the same authors. That text covers material for both an undergraduate and graduate course, while this book builds on and expands the graduate-level material. Features Extensive exercises and applications. Flexibility: appropriate for either a first course at the graduate level or an advanced course at the undergraduate level. Opens avenues to a variety of research areas in graph theory. Emphasis on topological and algebraic graph theory.
Download or read book Topics in Graph Theory written by Wilfried Imrich and published by CRC Press. This book was released on 2008-10-27 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way,
Download or read book Topics in Topological Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2009-07-09 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen 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 and the topology of surfaces. Each chapter concludes with an extensive list of references.
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.
Download or read book Algebra Graph Theory and their Applications written by T.T Chelvam and published by ALPHA SCIENCE INTERNATIONAL LIMITED. This book was released on 2009-12-03 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra and Graph Theory are two fascinating branches of Mathematics. The tools of each have been used in the other to explore and investigate problems in depth. Especially the Cayley graphs constructed out of the group structures have been greatly and extensively used in Parallel computers to provide network to the routing problem. ALGEBRA, GRAPH THEORY AND THEIR APPLICATIONS takes an inclusive view of the two areas and presents a wide range of topics. It includes sixteen referred research articles on algebra and graph theory of which three are expository in nature alongwith articles exhibiting the use of algebraic techniques in the study of graphs. A substantial proportion of the book covers topics that have not yet appeared in book form providing a useful resource to the younger generation of researchers in Discrete Mathematics.
Download or read book A Seminar on Graph Theory written by Frank Harary and published by Courier Dover Publications. This book was released on 2015-07-15 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures given in F. Harary's seminar course, University College of London, Dept. of Mathematics, 1962-1963.
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.
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
Download or read book Eigenspaces of Graphs written by Dragoš M. Cvetković and published by Cambridge University Press. This book was released on 1997-01-09 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research.
