Pdf ebook: Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs

Pdf download ebook Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs

Summary: On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are

  • Author : N.a
  • Publisher: CRC Press
  • ISBN: 1439863393
  • Genre: Computers
  • Number of Pages: 425
  • Language: English
  • Views: 729
  • Downloads: 729
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Description: On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o


Pdf ebook: Combinatorial Matrix Theory and Generalized Inverses of Matrices

Pdf download ebook Combinatorial Matrix Theory and Generalized Inverses of Matrices

Summary: This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and exposito

  • Author : Ravindra B. Bapat,Steve J. Kirkland,K. Manjunatha Prasad,Simo Puntanen
  • Publisher: Springer Science & Business Media
  • ISBN: 8132210530
  • Genre: Mathematics
  • Number of Pages: 277
  • Language: English
  • Views: 1478
  • Downloads: 1478
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Description: This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics: `matrices in graph theory', `generalized inverses of matrices', `matrix methods in statistics' and `magic squares'. In the area of matrices and graphs, speci_c topics addressed in this volume include energy of graphs, q-analog, immanants of matrices and graph realization of product of adjacency matrices. Topics in the book from `Matrix Methods in Statistics' are, for example, the analysis of BLUE via eigenvalues of covariance matrix, copulas, error orthogonal model, and orthogonal projectors in the linear regression models. Moore-Penrose inverse of perturbed operators, reverse order law in the case of inde_nite inner product space, approximation numbers, condition numbers, idempotent matrices, semiring of nonnegative matrices, regular matrices over incline and partial order of matrices are the topics addressed under the area of theory of generalized inverses. In addition to the above traditional topics and a report on CMTGIM 2012 as an appendix, we have an article on old magic squares from India.


Pdf ebook: Combinatorial Matrix Theory

Pdf download ebook Combinatorial Matrix Theory

Summary: This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in

  • Author : Richard A. Brualdi,Ángeles Carmona,P. van den Driessche,Stephen Kirkland,Dragan Stevanović
  • Publisher: Birkhäuser
  • ISBN: 3319709534
  • Genre: Mathematics
  • Number of Pages: 219
  • Language: English
  • Views: 1581
  • Downloads: 1581
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Description: This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.


Pdf ebook: Handbook of Graph Theory, Combinatorial Optimization, and Algorithms

Pdf download ebook Handbook of Graph Theory, Combinatorial Optimization, and Algorithms

Summary: The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book th

  • Author : Krishnaiyan "KT" Thulasiraman,Subramanian Arumugam,Andreas Brandstädt,Takao Nishizeki
  • Publisher: CRC Press
  • ISBN: 1420011073
  • Genre: Computers
  • Number of Pages: 1244
  • Language: English
  • Views: 1447
  • Downloads: 1447
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Description: The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both graph theory and c


Pdf ebook: Combinatorics of Permutations

Pdf download ebook Combinatorics of Permutations

Summary: A Unified Account of Permutations in Modern CombinatoricsA 2006 CHOICE Outstanding Academic Title, the first edition of this bestseller was lauded for its

  • Author : Miklos Bona
  • Publisher: CRC Press
  • ISBN: 1439850526
  • Genre: Computers
  • Number of Pages: 478
  • Language: English
  • Views: 1639
  • Downloads: 1639
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Description: A Unified Account of Permutations in Modern CombinatoricsA 2006 CHOICE Outstanding Academic Title, the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, Second Edition continues to clearly show the usefuln


Pdf ebook: Handbook of Graph Theory, Second Edition

Pdf download ebook Handbook of Graph Theory, Second Edition

Summary: In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting the

  • Author : Jonathan L. Gross,Jay Yellen,Ping Zhang
  • Publisher: CRC Press
  • ISBN: 1439880190
  • Genre: Mathematics
  • Number of Pages: 1630
  • Language: English
  • Views: 1185
  • Downloads: 1185
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Description: In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition—over 400 pages longer than its predecessor—incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.


Pdf ebook: Group Inverses of M-Matrices and Their Applications

Pdf download ebook Group Inverses of M-Matrices and Their Applications

Summary: Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electr

  • Author : Stephen J. Kirkland,Michael Neumann
  • Publisher: CRC Press
  • ISBN: 1439888590
  • Genre: Mathematics
  • Number of Pages: 332
  • Language: English
  • Views: 1844
  • Downloads: 1844
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Description: Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix functions and apply the formulas to matrices arising in a demographic setting, including the class of Leslie matrices. With a focus on Markov chains, the text shows how the group inverse of an appropriate M-matrix is used in the perturbation analysis of the stationary distribution vector as well as in the derivation of a bound for the asymptotic convergence rate of the underlying Markov chain. It also illustrates how to use the group inverse to compute and analyze the mean first passage matrix for a Markov chain. The final chapters focus on the Laplacian matrix for an undirected graph and compare approaches for computing the group inverse. Collecting diverse results into a single volume, this self-contained book emphasizes the connections between problems arising in Markov chains, Perron eigenvalue analysis, and spectral graph theory. It shows how group inverses offer valuable insight into each of these areas.


Pdf ebook: Combinatorics of Set Partitions

Pdf download ebook Combinatorics of Set Partitions

Summary: Focusing on a very active area of mathematical research in the last decade, Combinatorics of Set Partitions presents methods used in the combinatorics of p

  • Author : Toufik Mansour
  • Publisher: CRC Press
  • ISBN: 1439863342
  • Genre: Computers
  • Number of Pages: 516
  • Language: English
  • Views: 1563
  • Downloads: 1563
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Description: Focusing on a very active area of mathematical research in the last decade, Combinatorics of Set Partitions presents methods used in the combinatorics of pattern avoidance and pattern enumeration in set partitions. Designed for students and researchers in discrete mathematics, the book is a one-stop reference on the results and research activities


Pdf ebook: Crossing Numbers of Graphs

Pdf download ebook Crossing Numbers of Graphs

Summary: Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field

  • Author : Marcus Schaefer
  • Publisher: CRC Press
  • ISBN: 1498750508
  • Genre: Mathematics
  • Number of Pages: 350
  • Language: English
  • Views: 1073
  • Downloads: 1073
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Description: Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science. The first part of the text deals with traditional crossing number, crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, and the independent odd crossing number.It also includes applications of the crossing number outside topological graph theory. Aimed at graduate students and professionals in both mathematics and computer science The first book of its kind devoted to the topic Authored by a noted authority in crossing numbers


Pdf ebook: Handbook of Finite State Based Models and Applications

Pdf download ebook Handbook of Finite State Based Models and Applications

Summary: Applicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata

  • Author : Jiacun Wang
  • Publisher: CRC Press
  • ISBN: 1439846197
  • Genre: Computers
  • Number of Pages: 409
  • Language: English
  • Views: 684
  • Downloads: 684
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Description: Applicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering. Handbook of Finite State Based Models and Applications provides a complete collection of introductory materials on fini


Pdf ebook: Handbook of Graph Drawing and Visualization

Pdf download ebook Handbook of Graph Drawing and Visualization

Summary: Get an In-Depth Understanding of Graph Drawing Techniques, Algorithms, Software, and ApplicationsThe Handbook of Graph Drawing and Visualization provides a

  • Author : Roberto Tamassia
  • Publisher: CRC Press
  • ISBN: 1420010263
  • Genre: Computers
  • Number of Pages: 862
  • Language: English
  • Views: 748
  • Downloads: 748
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Description: Get an In-Depth Understanding of Graph Drawing Techniques, Algorithms, Software, and ApplicationsThe Handbook of Graph Drawing and Visualization provides a broad, up-to-date survey of the field of graph drawing. It covers topological and geometric foundations, algorithms, software systems, and visualization applications in business, education, scie


Pdf ebook: Introduction to Combinatorics

Pdf download ebook Introduction to Combinatorics

Summary: What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or a

  • Author : Walter D. Wallis,John C. George
  • Publisher: CRC Press
  • ISBN: 1498777635
  • Genre: Mathematics
  • Number of Pages: 424
  • Language: English
  • Views: 1623
  • Downloads: 1623
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Description: What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM


Pdf ebook: Handbook of Enumerative Combinatorics

Pdf download ebook Handbook of Enumerative Combinatorics

Summary: Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today’s most prominent researchers. The contributo

  • Author : Miklos Bona
  • Publisher: CRC Press
  • ISBN: 1482220865
  • Genre: Mathematics
  • Number of Pages: 1086
  • Language: English
  • Views: 369
  • Downloads: 369
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Description: Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today’s most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods. This important new work is edited by Miklós Bóna of the University of Florida where he is a member of the Academy of Distinguished Teaching Scholars. He received his Ph.D. in mathematics at Massachusetts Institute of Technology in 1997. Miklós is the author of four books and more than 65 research articles, including the award-winning Combinatorics of Permutations. Miklós Bóna is an editor-in-chief for the Electronic Journal of Combinatorics and Series Editor of the Discrete Mathematics and Its Applications Series for CRC Press/Chapman and Hall. The first two chapters provide a comprehensive overview of the most frequently used methods in combinatorial enumeration, including algebraic, geometric, and analytic methods. These chapters survey generating functions, methods from linear algebra, partially ordered sets, polytopes, hyperplane arrangements, and matroids. Subsequent chapters illustrate applications of these methods for counting a wide array of objects. The contributors for this book represent an international spectrum of researchers with strong histories of results. The chapters are organized so readers advance from the more general ones, namely enumeration methods, towards the more specialized ones. Topics include coverage of asymptotic normality in enumeration, planar maps, graph enumeration, Young tableaux, unimodality, log-concavity, real zeros, asymptotic normality, trees, generalized Catalan paths, computerized enumeration schemes, enumeration of various graph classes, words, tilings, pattern avoidance, computer algebra, and parking functions. This book will be beneficial to a wide audience. It will appeal to experts on the topic interested in learning more about the finer points, readers interested in a systematic and organized treatment of the topic, and novices who are new to the field.


Pdf ebook: Handbook of Discrete and Combinatorial Mathematics

Pdf download ebook Handbook of Discrete and Combinatorial Mathematics

Summary: Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as

  • Author : Kenneth H. Rosen
  • Publisher: CRC Press
  • ISBN: 1584887818
  • Genre: Mathematics
  • Number of Pages: 1612
  • Language: English
  • Views: 1353
  • Downloads: 1353
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Description: Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.


Pdf ebook: Quantitative Graph Theory

Pdf download ebook Quantitative Graph Theory

Summary: The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstr

  • Author : Matthias Dehmer,Frank Emmert-Streib
  • Publisher: CRC Press
  • ISBN: 1466584521
  • Genre: Computers
  • Number of Pages: 528
  • Language: English
  • Views: 760
  • Downloads: 760
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Description: The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical technique


Pdf ebook: Representation Theory of Symmetric Groups

Pdf download ebook Representation Theory of Symmetric Groups

Summary: Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utiliz

  • Author : Pierre-Loic Meliot
  • Publisher: CRC Press
  • ISBN: 1498719139
  • Genre: Mathematics
  • Number of Pages: 666
  • Language: English
  • Views: 1837
  • Downloads: 1837
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Description: Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint. This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra. In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups. Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.


Pdf ebook: Handbook of Finite Fields

Pdf download ebook Handbook of Finite Fields

Summary: Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields.

  • Author : Gary L. Mullen,Daniel Panario
  • Publisher: CRC Press
  • ISBN: 1439873828
  • Genre: Computers
  • Number of Pages: 1068
  • Language: English
  • Views: 1171
  • Downloads: 1171
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Description: Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and


Pdf ebook: Introduction to Coding Theory

Pdf download ebook Introduction to Coding Theory

Summary: This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for

  • Author : Jurgen Bierbrauer
  • Publisher: CRC Press
  • ISBN: 148229981X
  • Genre: Computers
  • Number of Pages: 512
  • Language: English
  • Views: 1421
  • Downloads: 1421
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Description: This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.


Pdf ebook: Introduction to Enumerative and Analytic Combinatorics

Pdf download ebook Introduction to Enumerative and Analytic Combinatorics

Summary: Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enum

  • Author : Miklos Bona
  • Publisher: CRC Press
  • ISBN: 1482249103
  • Genre: Computers
  • Number of Pages: 534
  • Language: English
  • Views: 1526
  • Downloads: 1526
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Description: Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares. Strengthening the analytic flavor of the book, this Second Edition: Features a new chapter on analytic combinatorics and new sections on advanced applications of generating functions Demonstrates powerful techniques that do not require the residue theorem or complex integration Adds new exercises to all chapters, significantly extending coverage of the given topics Introduction to Enumerative and Analytic Combinatorics, Second Edition makes combinatorics more accessible, increasing interest in this rapidly expanding field. Outstanding Academic Title of the Year, Choice magazine, American Library Association.


Pdf ebook: Graphs, Algorithms, and Optimization

Pdf download ebook Graphs, Algorithms, and Optimization

Summary: The second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, bu

  • Author : William Kocay,Donald L. Kreher
  • Publisher: CRC Press
  • ISBN: 1482251183
  • Genre: Mathematics
  • Number of Pages: 546
  • Language: English
  • Views: 375
  • Downloads: 375
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Description: The second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs.