Download or read book Some Problems in the Theory of Distance regular Graphs written by Benjamin V. C. Collins and published by . This book was released on 1996 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Distance Regular Graphs written by Andries E. Brouwer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Regular Graphs written by Zoran Stanić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-24 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Distance In Graphs written by Fred Buckley and published by Addison Wesley Publishing Company. This book was released on 1990-01-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectra of Graphs written by Andries E. Brouwer and published by Springer Science & Business Media. This book was released on 2011-12-17 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.
Download or read book On Some Spectral and Combinatorial Properties of Distance regular Graphs and Their Generalizations written by Víctor Diego and published by . This book was released on 2018 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work we present the study we did in Graph Theory. In the firsts chapteres of the tesis we study the pieces of information that can be obtained from a graph: the spectrum of the adjacency matrix, the preintersection numbers, the predistance polynomials and the average number of closed walks. Some of this pieces of information are direct generalizations of the intersection numbers or the predistance polynomials defined in the distance-regular graphs. We prove that the multiple properties that these pieces of information have in distance-regular graphs hold also in their generalizations, and these properties can be applied to any other graph. We also prove that the distinct pieces of information (even if their nature is algebraic or combinatorial) are equivalent. That is, we can obtain each one of the pieces in terms of each other; proving in this way that the properties of the graph derived from each one of the pieces can be also obtained in terms of each one of the other. We dedicate a chapter of the tesis to describe completly the especific procedures with which obtain each piece of inforation in terms of the others. In this tesis we introduce the "distance mean-regular" graphs. These graphs are a generalization of the distance-regular graphs. In this occasion, we demand to the graph combinatorial properties and we generalizate the algebraic properties of the distance-regular graphs. We generalizate the spectrum of a graph to introduce the "pseudo-spectrum" and we generalizate the Bose-Mesner algebra in distinct matrix algebras. The study of these generalizations, as well as the study of the relation between them, give us combinatorial and algebraic properties. In the final part of the tesis we study the vertex-isoperimetric problem in the Johnson Graph J(n,m). We solve completly the problem for some particular cases: J(n,1), J(n,2), J(2m-2,m), as well as their symetrics J(n,n-2) and J(2m+2,m). The solution for these cases are the initial segments of the colexicographic order. This order is also the solution for small cardinals in every graph of this family, as well as for the asymptotic behaviour of the parameters n and m. However, this solution is not the optimal solution for every cardinal in every graph J(n,m). We prove and give an infinity family of counterexamples for which the initial segment of the colexicographic order is not optimal in terms of the vertex-isoperimetric problem.
Download or read book Strongly Regular Graphs written by Andries E. Brouwer and published by . This book was released on 2022-01-13 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.
Download or read book Recent Results in the Theory of Graph Spectra written by D.M. Cvetkovic and published by Elsevier. This book was released on 1988-01-01 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Designs and Their Codes written by E. F. Assmus and published by Cambridge University Press. This book was released on 1994-01-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.
Download or read book Algebraic Combinatorics written by Eiichi Bannai and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-02-22 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.
Download or read book Some Results on Bipartite Distance regular Graphs written by Michael S. Lang and published by . This book was released on 2001 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Erdos Ko Rado Theorems Algebraic Approaches written by Christopher Godsil and published by Cambridge University Press. This book was released on 2016 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate text focusing on algebraic methods that can be applied to prove the Erdős-Ko-Rado Theorem and its generalizations.
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 Graph Theory Singapore 1983 written by K.M. Koh and published by Springer. This book was released on 2006-11-14 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Integer Programming and Related Areas written by Rabe v. Randow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of integer programming and combinatorial optimization continue to be areas of great vitality, with an ever increasing number of publications and journals appearing. A classified bibliography thus continues to be necessary and useful today, even more so than it did when the project, of which this is the fifth volume, was started in 1970 in the Institut fur Okonometrie und Operations Research of the University of Bonn. The pioneering first volume was compiled by Claus Kastning during the years 1970 - 1975 and appeared in 1976 as Volume 128 of the series Lecture Notes in Economics and Mathematical Systems published by the Springer Verlag. Work on the project was continued by Dirk Hausmann, Reinhardt Euler, and Rabe von Randow, and resulted in the publication of the second, third, and fourth volumes in 1978, 1982, and 1985 (Volumes 160, 197, and 243 of the above series). The present book constitutes the fifth volume of the bibliography and covers the period from autumn 1984 to the end of 1987. It contains 5864 new publications by 4480 authors and was compiled by Rabe von Randow. Its form is practically identical to that of the first four volumes, some additions having been made to the subject list.
Download or read book Regular Graphs written by Zoran Stanić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-24 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
