A Beginner S Guide To Graph Theory
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A Beginner S Guide To Graph Theory
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Author : W.D. Wallis
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-08
A Beginner S Guide To Graph 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 2007-06-08 with Mathematics categories.
Concisely written, gentle introduction to graph theory suitable as a textbook or for self-study Graph-theoretic applications from diverse fields (computer science, engineering, chemistry, management science) 2nd ed. includes new chapters on labeling and communications networks and small worlds, as well as expanded beginner's material Many additional changes, improvements, and corrections resulting from classroom use
A Beginner S Guide To Discrete Mathematics
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Author : W.D. Wallis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
A Beginner S Guide To Discrete Mathematics 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 2013-03-14 with Mathematics categories.
This text is a basic introduction to those areas of discrete mathematics used by stu dents of mathematics and computer science. Introductory courses on this material are now standard at many colleges and universities. Usually these courses are of one semester's duration, and usually they are offered at the sophomore level. Very often this will be the first course where the students see several real proofs. The preparation of the students is very mixed, and one cannot assume a strong back ground. In particular, the instructor should not assume that the students have seen a linear algebra course, or any introduction to number systems that goes beyond college algebra. In view of this, I have tried to avoid too much sophistication, while still re taining rigor. I hope I have included enough problems so that the student can reinforce the concepts. Most of the problems are quite easy, with just a few dif ficult exercises scattered through the text. If the class is weak, a small number of sections will be too hard, while the instructor who has a strong class will need to include some supplementary material. I think this is preferable to a book at a higher mathematical level, which will scare away weaker students.
Expander Families And Cayley Graphs
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Author : Mike Krebs
language : en
Publisher: Oxford University Press
Release Date : 2011-09-30
Expander Families And Cayley Graphs written by Mike Krebs and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-30 with Mathematics categories.
The theory of expander graphs is a rapidly developing topic in mathematics and computer science, with applications to communication networks, error-correcting codes, cryptography, complexity theory, and much more. Expander Families and Cayley Graphs: A Beginner's Guide is a comprehensive introduction to expander graphs, designed to act as a bridge between classroom study and active research in the field of expanders. It equips those with little or no prior knowledge with the skills necessary to both comprehend current research articles and begin their own research. Central to this book are four invariants that measure the quality of a Cayley graph as a communications network-the isoperimetric constant, the second-largest eigenvalue, the diameter, and the Kazhdan constant. The book poses and answers three core questions: How do these invariants relate to one another? How do they relate to subgroups and quotients? What are their optimal values/growth rates? Chapters cover topics such as: · Graph spectra · A Cheeger-Buser-type inequality for regular graphs · Group quotients and graph coverings · Subgroups and Schreier generators · Ramanujan graphs and the Alon-Boppana theorem · The zig-zag product and its relation to semidirect products of groups · Representation theory and eigenvalues of Cayley graphs · Kazhdan constants The only introductory text on this topic suitable for both undergraduate and graduate students, Expander Families and Cayley Graphs requires only one course in linear algebra and one in group theory. No background in graph theory or representation theory is assumed. Examples and practice problems with varying complexity are included, along with detailed notes on research articles that have appeared in the literature. Many chapters end with suggested research topics that are ideal for student projects.
A Beginner S Guide To Finite Mathematics
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Author : W.D. Wallis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09
A Beginner S Guide To Finite Mathematics 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 2013-11-09 with Mathematics categories.
When elementary courses in discrete and combinatorial mathematics first became popular, they usually covered a broad spectrumofpure and applied topics. Most of the students were in Mathematics and Computer Science, with a handful ofbrave souls from other disciplines. Those other students usually found the courses quite difficult. However, the applications were useful in a numberofareas. The teaching of discrete topics has evolved into two streams. The more math ematical parts are studied in courses called Discrete Mathematics, and more ad vanced, more rigorous courses called Combinatorics, or named for specific areas (Graph Theory, Combinatorial Designs, Cryptography, and so on). Introductions to those areas of applicable discrete mathematics used by students in business, management and the social sciences are usually called Finite Mathematics, and e1ementary courses on this material are now standard at many colleges and uni versities.These courses are typically offered at the freshman level although many students take them later in their careers.
Pancyclic And Bipancyclic Graphs
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Author : John C. George
language : en
Publisher: Springer
Release Date : 2016-05-18
Pancyclic And Bipancyclic Graphs written by John C. George and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-18 with Mathematics categories.
This book is focused on pancyclic and bipancyclic graphs and is geared toward researchers and graduate students in graph theory. Readers should be familiar with the basic concepts of graph theory, the definitions of a graph and of a cycle. Pancyclic graphs contain cycles of all possible lengths from three up to the number of vertices in the graph. Bipartite graphs contain only cycles of even lengths, a bipancyclic graph is defined to be a bipartite graph with cycles of every even size from 4 vertices up to the number of vertices in the graph. Cutting edge research and fundamental results on pancyclic and bipartite graphs from a wide range of journal articles and conference proceedings are composed in this book to create a standalone presentation. The following questions are highlighted through the book: - What is the smallest possible number of edges in a pancyclic graph with v vertices? - When do pancyclic graphs exist with exactly one cycle of every possible length? - What is the smallest possible number of edges in a bipartite graph with v vertices? - When do bipartite graphs exist with exactly one cycle of every possible length?
Data Centric Artificial Intelligence A Beginner S Guide
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Author : Parikshit N. Mahalle
language : en
Publisher: Springer Nature
Release Date : 2023-10-10
Data Centric Artificial Intelligence A Beginner S Guide written by Parikshit N. Mahalle and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-10 with Technology & Engineering categories.
This book discusses the best research roadmaps, strategies, and challenges in data-centric approach of artificial intelligence (AI) in various domains. It presents comparative studies of model-centric and data-centric AI. It also highlights different phases in data-centric approach and data-centric principles. The book presents prominent use cases of data-centric AI. It serves as a reference guide for researchers and practitioners in academia and industry.
Combinatorics For Beginners A Comprehensive Guide To The Fundamentals
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-19
Combinatorics For Beginners A Comprehensive Guide To The Fundamentals written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-19 with Mathematics categories.
Step into the captivating world of combinatorics, a branch of mathematics that unveils the patterns and relationships hidden within finite and discrete structures. "Combinatorics for Beginners: A Comprehensive Guide to the Fundamentals" is an accessible and engaging introduction to this fascinating subject, guiding you through the intricacies of counting techniques, permutations and combinations, binomial coefficients, Pascal's triangle, and their diverse applications. Delve into the realm of graph theory, exploring the intricacies of trees, forests, Eulerian and Hamiltonian graphs, planar graphs, and graph coloring. Unravel the complexities of network flows, delving into maximum flow problems, Ford-Fulkerson algorithm, Edmond-Karp algorithm, push-relabel algorithm, and their practical applications. Discover the elegance of matching theory, including bipartite matching, perfect matching, maximum matching, and their far-reaching applications. Immerse yourself in the world of matroids, exploring linear matroids, graphic matroids, polymatroids, and their captivating applications. Conquer the challenges of linear programming, mastering the simplex method, duality theorem, sensitivity analysis, and their wide-ranging applications. Embark on a quest to understand combinatorial optimization, exploring the traveling salesman problem, knapsack problem, scheduling problems, and their diverse applications. Delve into the realm of approximation algorithms, unraveling the intricacies of greedy algorithms, local search algorithms, randomized algorithms, and their practical applications. Finally, confront the complexities of NP-completeness, gaining insights into NP-complete problems, NP-hard problems, reductions, and their far-reaching applications. Written with clarity and precision, this comprehensive guide is an invaluable resource for students, researchers, and practitioners seeking a thorough understanding of combinatorics. Enriched with thought-provoking problems and exercises, this book reinforces your understanding of the concepts and techniques presented. "Combinatorics for Beginners: A Comprehensive Guide to the Fundamentals" is your gateway to unlocking the secrets of combinatorics, empowering you to solve complex problems, optimize solutions, and gain a deeper appreciation for the elegance and beauty of mathematics. If you like this book, write a review!
Combinatorial Mathematics
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Author : Douglas B. West
language : en
Publisher: Cambridge University Press
Release Date : 2021
Combinatorial Mathematics written by Douglas B. West 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 2021 with Mathematics categories.
This is the most readable and thorough graduate textbook and reference for combinatorics, covering enumeration, graphs, sets, and methods.
Magic Graphs
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Author : Alison M. Marr
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-06
Magic Graphs written by Alison M. Marr 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 2012-11-06 with Mathematics categories.
Magic squares are among the more popular mathematical recreations. Over the last 50 years, many generalizations of “magic” ideas have been applied to graphs. Recently there has been a resurgence of interest in “magic labelings” due to a number of results that have applications to the problem of decomposing graphs into trees. Key features of this second edition include: · a new chapter on magic labeling of directed graphs · applications of theorems from graph theory and interesting counting arguments · new research problems and exercises covering a range of difficulties · a fully updated bibliography and index This concise, self-contained exposition is unique in its focus on the theory of magic graphs/labelings. It may serve as a graduate or advanced undergraduate text for courses in mathematics or computer science, and as reference for the researcher.
Introduction To Computational Social Science
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Author : Claudio Cioffi-Revilla
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-31
Introduction To Computational Social Science written by Claudio Cioffi-Revilla 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 2013-12-31 with Computers categories.
This reader-friendly textbook is the first work of its kind to provide a unified Introduction to Computational Social Science (CSS). Four distinct methodological approaches are examined in detail, namely automated social information extraction, social network analysis, social complexity theory and social simulation modeling. The coverage of these approaches is supported by a discussion of the historical context, as well as by a list of texts for further reading. Features: highlights the main theories of the CSS paradigm as causal explanatory frameworks that shed new light on the nature of human and social dynamics; explains how to distinguish and analyze the different levels of analysis of social complexity using computational approaches; discusses a number of methodological tools; presents the main classes of entities, objects and relations common to the computational analysis of social complexity; examines the interdisciplinary integration of knowledge in the context of social phenomena.