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Author: Ravindra B. Bapat Publisher: Springer ISBN: 1447165691 Category : Mathematics Languages : en Pages : 193
Book Description
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: Ravindra B. Bapat Publisher: Springer ISBN: 1447165691 Category : Mathematics Languages : en Pages : 193
Book Description
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: Chris Godsil Publisher: Springer Science & Business Media ISBN: 1461301637 Category : Mathematics Languages : en Pages : 453
Book Description
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: Norman Biggs Publisher: Cambridge University Press ISBN: 9780521458979 Category : Mathematics Languages : en Pages : 220
Book Description
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.
Author: Ulrich Knauer Publisher: Walter de Gruyter ISBN: 311025509X Category : Mathematics Languages : en Pages : 325
Book Description
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: Gareth A. Jones Publisher: Springer Nature ISBN: 3030328082 Category : Mathematics Languages : en Pages : 234
Book Description
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: Hartmut Ehrig Publisher: Springer Science & Business Media ISBN: 3540311882 Category : Computers Languages : en Pages : 383
Book Description
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.
Author: Lowell W. Beineke Publisher: Cambridge University Press ISBN: 1107079454 Category : Mathematics Languages : en Pages :
Book Description
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.
Author: Bela Bollobas Publisher: Springer Science & Business Media ISBN: 1461206197 Category : Mathematics Languages : en Pages : 408
Book Description
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: Courtney Brown Publisher: SAGE ISBN: 1412941091 Category : Mathematics Languages : en Pages : 105
Book Description
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.
Author: Ravindra B. Bapat
Author: Ravindra B. Bapat
Author: Chris Godsil
Author: Norman Biggs
Author: Lowell W. Beineke
Author: Ulrich Knauer
Author: Gareth A. Jones
Author: Hartmut Ehrig
Author: Lowell W. Beineke
Author: Bela Bollobas
Author: Courtney Brown