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Author : László Lovász,Vera T. Sós
Publisher : Unknown
Page : 412 pages
File Size : 50,8 Mb
Release : 1981
Category : Algebra
ISBN : UCSD:31822001199058
Author : Gena Hahn,Gert Sabidussi
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 43,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401589376
The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.
Author : László Lovász,Vera T. Sós
Publisher : Unknown
Page : 443 pages
File Size : 40,9 Mb
Release : 1981
Category : Electronic
ISBN : 9638021403
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 49,8 Mb
Release : 1981
Category : Electronic
ISBN : OCLC:630904199
Author : Norman Biggs
Publisher : Cambridge University Press
Page : 220 pages
File Size : 41,8 Mb
Release : 1993
Category : Mathematics
ISBN : 0521458978
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 : Gareth A. Jones,Ilia Ponomarenko,Jozef Širáň
Publisher : Springer Nature
Page : 234 pages
File Size : 45,9 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 : Lowell W. Beineke,Robin J. Wilson
Publisher : Cambridge University Press
Page : 302 pages
File Size : 49,8 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 : Christopher Godsil,Karen Meagher
Publisher : Cambridge University Press
Page : 353 pages
File Size : 41,8 Mb
Release : 2016
Category : Mathematics
ISBN : 9781107128446
Graduate text focusing on algebraic methods that can be applied to prove the Erdős-Ko-Rado Theorem and its generalizations.
Author : Raina Robeva
Publisher : Academic Press
Page : 382 pages
File Size : 43,6 Mb
Release : 2015-05-09
Category : Mathematics
ISBN : 9780128012710
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
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 : Chris Godsil,Gordon F. Royle
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 53,5 Mb
Release : 2001-04-20
Category : Mathematics
ISBN : 0387952209
This book is primarily aimed at graduate students and researchers in graph theory, combinatorics, or discrete mathematics in general. However, all the necessary graph theory is developed from scratch, so the only pre-requisite for reading it is a first course in linear algebra and a small amount of elementary group theory. It should be accessible to motivated upper-level undergraduates.
Author : Ulrich Knauer
Publisher : Walter de Gruyter
Page : 325 pages
File Size : 48,8 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 : Ulrich Knauer,Kolja Knauer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 349 pages
File Size : 44,5 Mb
Release : 2019-10-08
Category : Mathematics
ISBN : 9783110617368
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.
Author : K. Erciyes
Publisher : Springer Nature
Page : 229 pages
File Size : 52,5 Mb
Release : 2021-11-17
Category : Computers
ISBN : 9783030878863
This textbook discusses the design and implementation of basic algebraic graph algorithms, and algebraic graph algorithms for complex networks, employing matroids whenever possible. The text describes the design of a simple parallel matrix algorithm kernel that can be used for parallel processing of algebraic graph algorithms. Example code is presented in pseudocode, together with case studies in Python and MPI. The text assumes readers have a background in graph theory and/or graph algorithms.
Author : Marlos A. G. Viana,Ams Special Session on Algebraic Methods in Statistics,Donald St. P. Richards
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 40,6 Mb
Release : 2001
Category : Algebra
ISBN : 9780821826874
The 23 papers report recent developments in using the technique to help clarify the relationship between phenomena and data in a number of natural and social sciences. Among the topics are a coordinate-free approach to multivariate exponential families, some rank-based hypothesis tests for covariance structure and conditional independence, deconvolution density estimation on compact Lie groups, random walks on regular languages and algebraic systems of generating functions, and the extendibility of statistical models. There is no index. c. Book News Inc.