Download or read book Introduction to Graph and Hypergraph Theory written by Vitaly Ivanovich Voloshin and published by . This book was released on 2009 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking courses in graph theory, discrete mathematics, data structures, algorithms. It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant mathematics is required. The very basic facts from set theory, proof techniques and algorithms are sufficient to understand it; but even those are explained in the text. Structurally, the text is divided into two parts where Part II is the generalisation of Part I. The first part discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph colouring. The second part considers generalisations of Part I and discusses hypertrees, bipartite hypergraphs, hypercycles, chordal hypergraphs, planar hypergraphs and hypergraph colouring. There is an interaction between the parts and within the parts to show how ideas of generalisations work. The main point is to exhibit the ways of generalisations and interactions of mathematical concepts from the very simple to the most advanced. One of the features of this text is the duality of hypergraphs. This fundamental concept is missing in graph theory (and in its introductory teaching) because dual graphs are not properly graphs, they are hypergraphs. However, as Part II shows, the duality is a very powerful tool in understanding, simplifying and unifying many combinatorial relations; it is basically a look at the same structure from the opposite (vertices versus edges) point of view.
Download or read book Hypergraph Theory written by Alain Bretto and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have many other names such as set systems and families of sets. This work presents the theory of hypergraphs in its most original aspects, while also introducing and assessing the latest concepts on hypergraphs. The variety of topics, their originality and novelty are intended to help readers better understand the hypergraphs in all their diversity in order to perceive their value and power as mathematical tools. This book will be a great asset to upper-level undergraduate and graduate students in computer science and mathematics. It has been the subject of an annual Master's course for many years, making it also ideally suited to Master's students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It will also benefit scientists, engineers and anyone else who wants to understand hypergraphs theory.
Download or read book Introduction to Graph and Hypergraph Theory written by Vitaly Ivanovich Voloshin and published by . This book was released on 2009 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Graph Theory written by Khee Meng Koh and published by World Scientific. This book was released on 2007 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college.The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.
Download or read book Introduction To Graph Theory H3 Mathematics written by Khee-meng Koh and published by World Scientific Publishing Company. This book was released on 2007-03-15 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college.The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.
Download or read book Introduction to Graph Theory written by Vitaly Ivanovich Voloshin and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory is an important area of contemporary mathematics with many applications in computer science, genetics, chemistry, engineering, industry, business and in social sciences. It is a young science invented and developing for solving challenging problems of 'computerised' society for which traditional areas of mathematics such as algebra or calculus are powerless. This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking the courses in graph theory, discrete mathematics, data structures, algorithms.It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant mathematics is required. The very basic facts from set theory, proof techniques and algorithms are sufficient to understand it; but even those are explained in the text. The book discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph colouring.The reader is conducted from the simplest examples, definitions and concepts, step by step, towards an understanding of a few most fundamental facts in the field.
Download or read book Introduction to Random Graphs written by Alan Frieze and published by Cambridge University Press. This book was released on 2016 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.
Download or read book Fractional Graph Theory written by Edward R. Scheinerman and published by Courier Corporation. This book was released on 2013-04-29 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explains the general theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics: fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, fractional isomorphism, and more. 1997 edition.
Download or read book Hypergraph Theory in Wireless Communication Networks written by Hongliang Zhang and published by Springer. This book was released on 2017-07-24 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief focuses on introducing a novel mathematical framework, referred as hypergraph theory, to model and solve the multiple interferer scenarios for future wireless communication networks. First, in Chap. 1, the authors introduce the basic preliminaries of hypergraph theory in general, and develop two hypergraph based polynomial algorithms, i.e., hypergraph coloring and hypergraph clustering. Then, in Chaps. 2 and 3, the authors present two emerging applications of hypergraph coloring and hypergraph clustering in Device-to-Device (D2D) underlay communication networks, respectively, in order to show the advantages of hypergraph theory compared with the traditional graph theory. Finally, in Chap. 4, the authors discuss the limitations of using hypergraph theory in future wireless networks and briefly present some other potential applications. This brief introduces the state-of-the-art research on the hypergraph theory and its applications in wireless communications. An efficient framework is provided for the researchers, professionals and advanced level students who are interested in the radio resource allocation in the heterogeneous networks to solve the resource allocation and interference management problems.
Download or read book Hypergraphs written by C. Berge and published by Elsevier. This book was released on 1984-05-01 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory has proved to be an extremely useful tool for solving combinatorial problems in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations Research and Optimization. It is natural to attempt to generalise the concept of a graph, in order to attack additional combinatorial problems. The idea of looking at a family of sets from this standpoint took shape around 1960. In regarding each set as a ``generalised edge'' and in calling the family itself a ``hypergraph'', the initial idea was to try to extend certain classical results of Graph Theory such as the theorems of Turán and König. It was noticed that this generalisation often led to simplification; moreover, one single statement, sometimes remarkably simple, could unify several theorems on graphs. This book presents what seems to be the most significant work on hypergraphs.
Download or read book Hypergraphs and Designs written by Mario Gionfriddo and published by Nova Science Publishers. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial designs represent an important area of contemporary discrete mathematics closely related to such fields as finite geometries, regular graphs and multigraphs, factorisations of graphs, linear algebra, number theory, finite fields, group and quasigroup theory, Latin squares, and matroids. It has a history of more than 150 years when it started as a collection of unrelated problems. Nowadays the field is a well-developed theory with deep mathematical results and a wide range of applications in coding theory, cryptography, computer science, and other areas. In the most general setting, a combinatorial design consists of a ground set of elements and a collection of subsets of these elements satisfying some specific restrictions; the latter are often expressed in the language of graphs. On the other side, hypergraph theory is a relatively new field which started in early 60s of the last century as a generalization of graph theory. A hypergraph consists of a ground set of elements and a collection of subsets of these elements without any specific restrictions. In this sense the concept of hypergraph is more general than the concept of combinatorial design. While it started as a generalization of graph theory, hypergraph theory soon became a separate subject because many new properties have been discovered that miss or degenerate in graphs. Compared to graph theory, the language of hypergraphs not only allows us to formulate and solve more general problems, it also helps us to understand and solve several graph theory problems by simplifying and unifying many previously unrelated concepts. The main feature of this book is applying the hypergraph approach to the theory of combinatorial designs. An alternative title of it could be "Combinatorial designs as hypergraphs". There is no analogue to this book on the market. Its primary audience is researchers and graduate students taking courses in design theory, combinatorial geometry, finite geometry, discrete mathematics, graph theory, combinatorics, cryptography, information and coding theory, and similar areas. The aim of this book is to show the connection and mutual benefit between hypergraph theory and design theory. It does not intend to give a survey of all important results or methods in any of these subjects.
Download or read book Introductory Graph Theory written by Béla Andrásfai and published by . This book was released on 1977 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Graph Theory written by Gary Chartrand and published by McGraw-Hill Science, Engineering & Mathematics. This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic applications of graphs ands equations, differnetiation rules for exponentiation of exponentials ...
Download or read book Introduction to Graph Signal Processing written by Antonio Ortega and published by Cambridge University Press. This book was released on 2022-06-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An intuitive and accessible text explaining the fundamentals and applications of graph signal processing. Requiring only an elementary understanding of linear algebra, it covers both basic and advanced topics, including node domain processing, graph signal frequency, sampling, and graph signal representations, as well as how to choose a graph. Understand the basic insights behind key concepts and learn how graphs can be associated to a range of specific applications across physical, biological and social networks, distributed sensor networks, image and video processing, and machine learning. With numerous exercises and Matlab examples to help put knowledge into practice, and a solutions manual available online for instructors, this unique text is essential reading for graduate and senior undergraduate students taking courses on graph signal processing, signal processing, information processing, and data analysis, as well as researchers and industry professionals.
Download or read book Hyperedge Replacement Grammars and Languages written by Annegret Habel and published by Springer Science & Business Media. This book was released on 1992-12-08 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of graph grammars is theoretically attractive and well motivated byvarious applications. More than 20 years ago, the concept of graph grammars was introduced by A. Rosenfeld as a formulation of some problems in pattern recognition and image processing, as well as by H.J. Schneider as a method for data type specification. Within graph-grammar theory one maydistinguish the set-theoretical approach, the algebraic approach, and the logical approach. These approaches differ in the method in which graph replacement is described. Specific approaches, node replacement and hyperedge replacement, concern the basic units of a hypergraph, nodes and hyperedges. This monograph is mainly concerned with the hyperedge-replacement approach. Hyperedge-replacement grammars are introduced as a device for generating hypergraph languages including graph languages and string languages. The concept combines a context-free rewriting with a comparatively large generative power. The volume includes a foreword by H. Ehrig.
Download or read book Introductory Graph Theory with Applications written by Fred Buckley and published by Waveland Press. This book was released on 2013-11-27 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory’s practical applications extend not only across multiple areas of mathematics and computer science but also throughout the social sciences, business, engineering, and other subjects. Buckley and Lewinter have written their text with students of all these disciplines in mind. Pedagogically rich, the authors provide hundreds of worked-out examples, figures, and exercises of varying degrees of difficulty. Concepts are presented in a readable and accessible manner, and applications are stressed throughout so the reader never loses sight of the powerful tools graph theory provides to solve real-world problems. Such diverse areas as job assignment, delivery truck routing, location of emergency or service facilities, network reliability, zoo design, exam scheduling, error-correcting codes, facility layout, and the critical path method are covered.
Download or read book A Beginner s Guide to Graph Theory written by W.D. Wallis and published by Springer Science & Business Media. This book was released on 2010-05-05 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
