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Author : Lowell W. Beineke,Robin J. Wilson
Publisher : Cambridge University Press
Page : 302 pages
File Size : 46,7 Mb
Release : 2004-10-04
Category : Mathematics
ISBN : 0521801974
There is no other book with such a wide scope of both areas of algebraic graph theory.
Author : Lowell W. Beineke,Senior Lecturer Faculty of Mathematics Robin J Wilson
Publisher : Unknown
Page : 296 pages
File Size : 53,7 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107089530
There is no other book with such a wide scope of both areas of algebraic graph theory.
Author : Chris Godsil,Gordon F. Royle
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 48,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461301639
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 : Jonathan L Gross,Jay Yellen,Mark Anderson
Publisher : CRC Press
Page : 904 pages
File Size : 54,7 Mb
Release : 2023-05-24
Category : Mathematics
ISBN : 9781000884081
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.
Author : Ravindra B. Bapat
Publisher : Springer
Page : 193 pages
File Size : 43,9 Mb
Release : 2014-09-19
Category : Mathematics
ISBN : 9781447165699
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.
Author : T.T Chelvam
Publisher : ALPHA SCIENCE INTERNATIONAL LIMITED
Page : 370 pages
File Size : 47,6 Mb
Release : 2009-12-03
Category : Mathematics
ISBN : 9788184873108
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.
Author : Gareth A. Jones,Ilia Ponomarenko,Jozef Širáň
Publisher : Springer Nature
Page : 234 pages
File Size : 53,9 Mb
Release : 2020-01-10
Category : Mathematics
ISBN : 9783030328085
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.
Author : Ulrich Knauer
Publisher : Walter de Gruyter
Page : 325 pages
File Size : 52,6 Mb
Release : 2011-09-29
Category : Mathematics
ISBN : 9783110255096
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.
Author : Richard P. Stanley
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 47,8 Mb
Release : 2013-06-17
Category : Mathematics
ISBN : 9781461469988
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.
Author : Bela Bollobas
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 47,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461206194
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.
Author : Yanpei Liu
Publisher : Walter de Gruyter GmbH & Co KG
Page : 422 pages
File Size : 55,8 Mb
Release : 2017-09-11
Category : Mathematics
ISBN : 9783110480757
This book studies algebraic representations of graphs in order to investigate combinatorial structures via local symmetries. Topological, combinatorial and algebraic classifications are distinguished by invariants of polynomial type and algorithms are designed to determine all such classifications with complexity analysis. Being a summary of the author‘s original work on graph embeddings, this book is an essential reference for researchers in graph theory. Contents Abstract Graphs Abstract Maps Duality Orientability Orientable Maps Nonorientable Maps Isomorphisms of Maps Asymmetrization Asymmetrized Petal Bundles Asymmetrized Maps Maps within Symmetry Genus Polynomials Census with Partitions Equations with Partitions Upper Maps of a Graph Genera of a Graph Isogemial Graphs Surface Embeddability
Author : Lowell W. Beineke,Robin J. Wilson
Publisher : Cambridge University Press
Page : 346 pages
File Size : 52,9 Mb
Release : 2012-11-08
Category : Mathematics
ISBN : 9781107244306
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.
Author : Wilfried Imrich,Sandi Klavzar,Douglas F Rall
Publisher : CRC Press
Page : 219 pages
File Size : 43,9 Mb
Release : 2008-10-27
Category : Mathematics
ISBN : 9781439865330
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,
Author : Frank Harary
Publisher : Courier Dover Publications
Page : 129 pages
File Size : 40,6 Mb
Release : 2015-07-15
Category : Mathematics
ISBN : 9780486796840
Lectures given in F. Harary's seminar course, University College of London, Dept. of Mathematics, 1962-1963.
Author : Lowell W. Beineke,Robin J. Wilson
Publisher : Cambridge University Press
Page : 366 pages
File Size : 54,8 Mb
Release : 2009-07-09
Category : Mathematics
ISBN : 052180230X
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.