Graphs, Matrices, and Designs

Graphs, Matrices, and Designs
Author: Rees
Publisher: Routledge
Total Pages: 273
Release: 2017-07-12
Genre: Mathematics
ISBN: 1351444379

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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 and Matrices

Graphs and Matrices
Author: Ravindra B. Bapat
Publisher: Springer
Total Pages: 197
Release: 2014-09-19
Genre: Mathematics
ISBN: 1447165691

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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.

Design Structure Matrix Methods and Applications

Design Structure Matrix Methods and Applications
Author: Steven D. Eppinger
Publisher: MIT Press
Total Pages: 352
Release: 2012-05-25
Genre: Science
ISBN: 0262300656

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An introduction to a powerful and flexible network modeling tool for developing and understanding complex systems, with many examples from a range of industries. Design structure matrix (DSM) is a straightforward and flexible modeling technique that can be used for designing, developing, and managing complex systems. DSM offers network modeling tools that represent the elements of a system and their interactions, thereby highlighting the system's architecture (or designed structure). Its advantages include compact format, visual nature, intuitive representation, powerful analytical capacity, and flexibility. Used primarily so far in the area of engineering management, DSM is increasingly being applied to complex issues in health care management, financial systems, public policy, natural sciences, and social systems. This book offers a clear and concise explanation of DSM methods for practitioners and researchers.

Graph Theory and Sparse Matrix Computation

Graph Theory and Sparse Matrix Computation
Author: Alan George
Publisher: Springer Science & Business Media
Total Pages: 254
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461383692

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When reality is modeled by computation, matrices are often the connection between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix, the better the answer, however, efficiency demands that every possible advantage be exploited. The articles in this volume are based on recent research on sparse matrix computations. This volume looks at graph theory as it connects to linear algebra, parallel computing, data structures, geometry, and both numerical and discrete algorithms. The articles are grouped into three general categories: graph models of symmetric matrices and factorizations, graph models of algorithms on nonsymmetric matrices, and parallel sparse matrix algorithms. This book will be a resource for the researcher or advanced student of either graphs or sparse matrices; it will be useful to mathematicians, numerical analysts and theoretical computer scientists alike.

Graphs, Codes and Designs

Graphs, Codes and Designs
Author: P. J. Cameron
Publisher: Cambridge University Press
Total Pages: 157
Release: 1980-07-31
Genre: Mathematics
ISBN: 0521231418

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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.

Matrices and Graphs in Geometry

Matrices and Graphs in Geometry
Author: Miroslav Fiedler
Publisher: Cambridge University Press
Total Pages: 206
Release: 2011-02-03
Genre: Mathematics
ISBN: 0521461936

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Demonstrates the close relationship between matrix theory and elementary Euclidean geometry, with emphasis on using simple graph-theoretical notions.

Matrices in Combinatorics and Graph Theory

Matrices in Combinatorics and Graph Theory
Author: Bolian Liu
Publisher: Springer Science & Business Media
Total Pages: 326
Release: 2000-10-31
Genre: Mathematics
ISBN: 9780792364696

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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.

Combinatorial Configurations

Combinatorial Configurations
Author: Vladimir Tonchev
Publisher: Longman Scientific and Technical
Total Pages: 216
Release: 1988
Genre: Mathematics
ISBN:

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Matrices and Graphs Stability Problems in Mathematical Ecology

Matrices and Graphs Stability Problems in Mathematical Ecology
Author: D. Logofet
Publisher: CRC Press
Total Pages: 388
Release: 2018-02-01
Genre: Science
ISBN: 1351091220

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Intuitive ideas of stability in dynamics of a biological population, community, or ecosystem can be formalized in the framework of corresponding mathematical models. These are often represented by systems of ordinary differential equations or difference equations. Matrices and Graphs covers achievements in the field using concepts from matrix theory and graph theory. The book effectively surveys applications of mathematical results pertinent to issues of theoretical and applied ecology. The only mathematical prerequisite for using Matrices and Graphs is a working knowledge of linear algebra and matrices. The book is ideal for biomathematicians, ecologists, and applied mathematicians doing research on dynamic behavior of model populations and communities consisting of multi-component systems. It will also be valuable as a text for a graduate-level topics course in applied math or mathematical ecology.

Graph Theory

Graph Theory
Author: B Andrasfai
Publisher: CRC Press
Total Pages: 298
Release: 1991-01-01
Genre: Mathematics
ISBN: 9780852742228

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Graph Theory: Flows, Matrices covers a number of topics in graph theory that are important in the major areas of application. It provides graph theoretic tools that can be readily and efficiently applied to problems in operational research, computer science, electrical engineering, and economics. Emphasizing didactic principles, the book derives theorems and proofs from a detailed analysis of the structure of graphs. The easy-to-follow algorithms can be readily converted to computer codes in high-level programming languages. Requiring knowledge of the basic concepts of graph theory and a familiarity with some simple results, the book also includes 100 exercises with solutions to help readers gain experience and 131 diagrams to aid in the understanding of concepts and proofs.