Graphs Matrices And Designs
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Graphs Matrices And Designs
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Author : Rees
language : en
Publisher: Routledge
Release Date : 2017-07-12
Graphs Matrices And Designs written by Rees and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Mathematics categories.
Examines partitions and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph theory, Hadamard matrices and graph factorizations. This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers.
Graphs Codes And Designs
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Author : P. J. Cameron
language : en
Publisher: Cambridge University Press
Release Date : 1980-07-31
Graphs Codes And Designs written by P. J. Cameron 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 1980-07-31 with Mathematics categories.
This book is concerned with the relations between graphs, error-correcting codes and designs, in particular how techniques of graph theory and coding theory can give information about designs. A major revision and expansion of a previous volume in this series, this account includes many examples and new results as well as improved treatments of older material. So that non-specialists will find the treatment accessible the authors have included short introductions to the three main topics. This book will be welcomed by graduate students and research mathematicians and be valuable for advanced courses in finite combinatorics.
Groups And Graphs Designs And Dynamics
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Author : R. A. Bailey
language : en
Publisher: Cambridge University Press
Release Date : 2024-05-30
Groups And Graphs Designs And Dynamics written by R. A. Bailey 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 2024-05-30 with Mathematics categories.
This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
Graph Designs Hadamard Matrices And Geometric Configurations
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Author : Jan Kratochvíl
language : en
Publisher:
Release Date : 1997
Graph Designs Hadamard Matrices And Geometric Configurations written by Jan Kratochvíl 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.
Combinatorial Configurations
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Author : Vladimir Tonchev
language : en
Publisher: Longman Scientific and Technical
Release Date : 1988
Combinatorial Configurations written by Vladimir Tonchev and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Graphs And Matrices
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Author : Ravindra B. Bapat
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-23
Graphs And Matrices written by Ravindra B. Bapat 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 2010-07-23 with Mathematics categories.
Graphs and Matrices provides a welcome addition to the rapidly expanding selection of literature in this field. As the title suggests, the book’s primary focus is graph theory, with an emphasis on topics relating to linear algebra and matrix theory. Information is presented at a relatively elementary level with the view of leading the student into further research. In the first part of the book matrix preliminaries are discussed and the basic properties of graph-associated matrices highlighted. Further topics include those of graph theory such as regular graphs and algebraic connectivity, Laplacian eigenvalues of threshold graphs, positive definite completion problem and graph-based matrix games. Whilst this book will be invaluable to researchers in graph theory, it may also be of benefit to a wider, cross-disciplinary readership.
Matrices In Combinatorics And Graph Theory
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Author : Bolian Liu
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-10-31
Matrices In Combinatorics And Graph Theory written by Bolian Liu 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 2000-10-31 with Mathematics categories.
Combinatorics and Matrix Theory have a symbiotic, or mutually beneficial, relationship. This relationship is discussed in my paper The symbiotic relationship of combinatorics and matrix theoryl where I attempted to justify this description. One could say that a more detailed justification was given in my book with H. J. Ryser entitled Combinatorial Matrix Theon? where an attempt was made to give a broad picture of the use of combinatorial ideas in matrix theory and the use of matrix theory in proving theorems which, at least on the surface, are combinatorial in nature. In the book by Liu and Lai, this picture is enlarged and expanded to include recent developments and contributions of Chinese mathematicians, many of which have not been readily available to those of us who are unfamiliar with Chinese journals. Necessarily, there is some overlap with the book Combinatorial Matrix Theory. Some of the additional topics include: spectra of graphs, eulerian graph problems, Shannon capacity, generalized inverses of Boolean matrices, matrix rearrangements, and matrix completions. A topic to which many Chinese mathematicians have made substantial contributions is the combinatorial analysis of powers of nonnegative matrices, and a large chapter is devoted to this topic. This book should be a valuable resource for mathematicians working in the area of combinatorial matrix theory. Richard A. Brualdi University of Wisconsin - Madison 1 Linear Alg. Applies., vols. 162-4, 1992, 65-105 2Camhridge University Press, 1991.
Matrices Of Graphs And Designs With Emphasis On Their Integral Eigen Pair Balance Characteristic
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Author : Carol Lynne Jessop
language : en
Publisher:
Release Date : 2014
Matrices Of Graphs And Designs With Emphasis On Their Integral Eigen Pair Balance Characteristic written by Carol Lynne Jessop and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Charts, diagrams, etc categories.
Computational And Constructive Design Theory
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Author : W.D. Wallis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Computational And Constructive Design Theory written by W.D. Wallis 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 2013-06-29 with Mathematics categories.
Over the last several years, there has been a significant increase in compu tational combinatorics. The most widely reported results were, of course, the proof of the Four Color Theorem and the proof that there is no projective plane of parameter 10. Although the computer was essential in both proofs, the only reason for this was the fact that life is short. The computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were just longer. Another important fact to notice is that both problems were theoretical, pure mathematical ones. The pursuit of the Four-Color Theorem has led to the development of whole branches of graph theory. The plane of parameter 10 is not an isolated case; its nonexistence is the first (and so far, the only) coun terexample to the conjecture that the Bruck-Chowla-Ryser conditions were necessary and sufficient for the existence of a symmetric balanced incomplete block design; the study of this problem has also led to a number of theoretical advances, including investigation of the relationship between codes and designs.
The Mutually Beneficial Relationship Of Graphs And Matrices
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Author : Richard A. Brualdi
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-07-06
The Mutually Beneficial Relationship Of Graphs And Matrices written by Richard A. Brualdi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-06 with Mathematics categories.
Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the matrix. Examples include the use of digraphs to obtain strong results on diagonal dominance and eigenvalue inclusion regions and the use of the Rado-Hall theorem to deduce properties of special classes of matrices. Going the other way, linear algebraic properties of one of the matrices associated with a graph can be used to obtain useful combinatorial information about the graph. The adjacency matrix and the Laplacian matrix are two well-known matrices associated to a graph, and their eigenvalues encode important information about the graph. Another important linear algebraic invariant associated with a graph is the Colin de Verdiere number, which, for instance, characterizes certain topological properties of the graph. This book is not a comprehensive study of graphs and matrices. The particular content of the lectures was chosen for its accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more.