Some Results On Bipartite Distance Regular Graphs
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Some Results On Bipartite Distance Regular Graphs
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Author : Michael S. Lang
language : en
Publisher:
Release Date : 2001
Some Results On Bipartite Distance Regular Graphs written by Michael S. Lang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Regular Graphs
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Author : Zoran Stanić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-04-24
Regular Graphs written by Zoran Stanić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-24 with Mathematics categories.
Written for mathematicians working with the theory of graph spectra, this (primarily theoretical) book presents relevant results considering the spectral properties of regular graphs. The book begins with a short introduction including necessary terminology and notation. The author then proceeds with basic properties, specific subclasses of regular graphs (like distance-regular graphs, strongly regular graphs, various designs or expanders) and determining particular regular graphs. Each chapter contains detailed proofs, discussions, comparisons, examples, exercises and also indicates possible applications. Finally, the author also includes some conjectures and open problems to promote further research. Contents Spectral properties Particular types of regular graph Determinations of regular graphs Expanders Distance matrix of regular graphs
Distance Regular Graphs
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Author : Andries E. Brouwer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Distance Regular Graphs written by Andries E. Brouwer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.
Bipartite Distance Regular Graphs
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Author : Brian Curtin
language : en
Publisher:
Release Date : 1996
Bipartite Distance Regular Graphs written by Brian Curtin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Some Problems In The Theory Of Distance Regular Graphs
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Author : Benjamin V. C. Collins
language : en
Publisher:
Release Date : 1996
Some Problems In The Theory Of Distance Regular Graphs written by Benjamin V. C. Collins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Homotopy And Distance Regular Graphs
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Author : Heather Ames Lewis
language : en
Publisher:
Release Date : 1997
Homotopy And Distance Regular Graphs written by Heather Ames Lewis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Bipartite Graphs And Their Applications
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Author : Armen S. Asratian
language : en
Publisher: Cambridge University Press
Release Date : 1998-07-13
Bipartite Graphs And Their Applications written by Armen S. Asratian and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-13 with Mathematics categories.
This is the first book which deals solely with bipartite graphs. Together with traditional material, the reader will also find many new and unusual results. Essentially all proofs are given in full; many of these have been streamlined specifically for this text. Numerous exercises of all standards have also been included. The theory is illustrated with many applications especially to problems in timetabling, Chemistry, Communication Networks and Computer Science. For the most part the material is accessible to any reader with a graduate understanding of mathematics. However, the book contains advanced sections requiring much more specialized knowledge, which will be of interest to specialists in combinatorics and graph theory.
Recent Results In The Theory Of Graph Spectra
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Author : D.M. Cvetkovic
language : en
Publisher: Elsevier
Release Date : 1988-01-01
Recent Results In The Theory Of Graph Spectra written by D.M. Cvetkovic and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978. The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1. The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2. Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.
Distance In Graphs
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Author : Fred Buckley
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1990-01-21
Distance In Graphs written by Fred Buckley and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-21 with Mathematics categories.
Algebraic Combinatorics
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Author : Chris Godsil
language : en
Publisher: Routledge
Release Date : 2017-10-19
Algebraic Combinatorics written by Chris Godsil and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.