Graph Theory And Decomposition
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Graph Theory And Decomposition
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Author : Jomon Kottarathil
language : en
Publisher: CRC Press
Release Date : 2024-04-10
Graph Theory And Decomposition written by Jomon Kottarathil and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-10 with Mathematics categories.
The book Graph Theory and Decomposition covers major areas of the decomposition of graphs. It is a three-part reference book with nine chapters that is aimed at enthusiasts as well as research scholars. It comprehends historical evolution and basic terminologies, and it deliberates on decompositions into cyclic graphs, such as cycle, digraph, and K4-e decompositions. In addition to determining the pendant number of graphs, it has a discourse on decomposing a graph into acyclic graphs like general tree, path, and star decompositions. It summarises another recently developed decomposition technique, which decomposes the given graph into multiple types of subgraphs. Major conjectures on graph decompositions are elaborately discussed. It alludes to a comprehensive bibliography that includes over 500 monographs and journal articles. It includes more than 500 theorems, around 100 definitions, 56 conjectures, 40 open problems, and an algorithm. The index section facilitates easy access to definitions, major conjectures, and named theorems. Thus, the book Graph Theory and Decomposition will be a great asset, we hope, in the field of decompositions of graphs and will serve as a reference book for all who are passionate about graph theory.
Graph Decompositions
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Author : Reinhard Diestel
language : en
Publisher:
Release Date : 1990
Graph Decompositions written by Reinhard Diestel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Language Arts & Disciplines categories.
Graph Decompositions is the first book on a topic that belongs mainly to infinite graph theory. It offers a complete account of the theory of simplicial decompositions of graphs, from its origins in the 1930s right up to present-day research. In addition to being one of the most important tools in infinite graph theory, simplicial decompositions may be seen as a model for any kind of structural graph decomposition. The currently topical tree-decompositions, for example, have their origin in simplicial decompositions. The text is centred around a few guiding problems and concepts, such as the existence and the uniqueness problem of simplicial decompositions into primes, or the concept of excluded minors as a means of identifying a desired structure.It attempts to give as authentic a picture as possible of research in progress. To this end, it includes discussions of examples, proof strategies on the formation of new concepts, as well as numerous exercises and open problems. Graph Decompositions should prove attractive to any graph theorist or other mathematician interested in a new area of research, as well as to the advanced student looking for a lively and inspiring account of how such research evolves.
Methods Of Graph Decompositions
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Author : Vadim Zverovich
language : en
Publisher: Oxford University Press
Release Date : 2024-08-06
Methods Of Graph Decompositions written by Vadim Zverovich 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 2024-08-06 with Mathematics categories.
In general terms, a graph decomposition is a partition of a graph into parts satisfying some special conditions. Methods of Graph Decompositions discusses some state-of-the-art decomposition methods of graph theory, which are highly instrumental when dealing with a number of fundamental concepts such as unigraphs, isomorphism, reconstruction conjectures, k-dimensional graphs, degree sequences, line graphs and line hypergraphs. The first part of the book explores the algebraic theory of graph decomposition, whose major idea is to define a binary operation that turns the set of graphs or objects derived from graphs into an algebraic semigroup. If an operation and a class of graphs are appropriately chosen, then, just as for integers, each graph has a unique factorization (or canonical decomposition) into a product of prime factors. The unique factorization property makes this type of decomposition especially efficient for problems associated with graph isomorphism, and several such examples are described in the book. Another topic is devoted to Krausz-type decompositions, that is, special coverings of graphs by cliques that are directly associated with representation of graphs as line graphs of hypergraphs. The book discusses various algorithmic and structural results associated with the existence, properties and applications of such decompositions. In particular, it demonstrates how Krausz-type decompositions are directly related to topological dimension, information complexity and self-similarity of graphs, thus allowing to establish links between combinatorics, general topology, information theory and studies of complex systems. The above topics are united by the role played in their development by Professor Regina Tyshkevich, and the book is a tribute to her memory. The book will be ideal for researchers, engineers and specialists, who are interested in fundamental problems of graph theory and proof techniques to tackle them.
Cycles And Rays
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Author : Gena Hahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Cycles And Rays written by Gena Hahn 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 2012-12-06 with Mathematics categories.
What is the "archetypal" image that comes to mind when one thinks of an infinite graph? What with a finite graph - when it is thought of as opposed to an infinite one? What structural elements are typical for either - by their presence or absence - yet provide a common ground for both? In planning the workshop on "Cycles and Rays" it had been intended from the outset to bring infinite graphs to the fore as much as possible. There never had been a graph theoretical meeting in which infinite graphs were more than "also rans", let alone one in which they were a central theme. In part, this is a matter of fashion, inasmuch as they are perceived as not readily lending themselves to applications, in part it is a matter of psychology stemming from the insecurity that many graph theorists feel in the face of set theory - on which infinite graph theory relies to a considerable extent. The result is that by and large, infinite graph theorists know what is happening in finite graphs but not conversely. Lack of knowledge about infinite graph theory can also be found in authoritative l sources. For example, a recent edition (1987) of a major mathematical encyclopaedia proposes to ". . . restrict [itself] to finite graphs, since only they give a typical theory". If anything, the reverse is true, and needless to say, the graph theoretical world knows better. One may wonder, however, by how much.
Graph Structure And Monadic Second Order Logic
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Author : Bruno Courcelle
language : en
Publisher: Cambridge University Press
Release Date : 2012-06-14
Graph Structure And Monadic Second Order Logic written by Bruno Courcelle 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 2012-06-14 with Mathematics categories.
The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
A Seminar On Graph Theory
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Author : Frank Harary
language : en
Publisher: Courier Dover Publications
Release Date : 2015-07-15
A Seminar On Graph Theory written by Frank Harary and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Mathematics categories.
Lectures given in F. Harary's seminar course, University College of London, Dept. of Mathematics, 1962-1963.
Theory Of 2 Structures The A Framework For Decomposition And Transformation Of Graphs
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Author : Andrzej Ehrenfeucht
language : en
Publisher: World Scientific Publishing Company
Release Date : 1999-08-30
Theory Of 2 Structures The A Framework For Decomposition And Transformation Of Graphs written by Andrzej Ehrenfeucht and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-30 with Mathematics categories.
The theory of 2-structures provides a convenient framework for decomposition and transformation of mathematical systems where one or several different binary relationships hold between the objects of the system. In particular, it forms a useful framework for decomposition and transformation of graphs.The decomposition methods presented in this book correspond closely to the top-down design methods studied in computer science. The transformation methods considered here have a natural interpretation in the dynamic evolution of certain kinds of communication networks. From the mathematical point of view, the clan decomposition method presented here, also known as modular decomposition or substitution decomposition, is closely related to the decomposition by quotients in algebra. The transformation method presented here is based on labelled 2-structures over groups, the theory of which generalizes the well-studied theory of switching classes of graphs.This book is both a text and a monograph. As a monograph, the results concerning the decomposition and transformation of 2-structures are presented in a unified way. In addition, detailed notes on references are provided at the end of each chapter. These notes allow the reader to trace the origin of many notions and results, and to browse through the literature in order to extend the material presented in the book.To facilitate its use as a textbook, there are numerous examples and exercises which provide an opportunity for the reader to check his or her understanding of the discussed material. Furthermore, the text begins with preliminaries on partial orders, semigroups, groups and graphs to the extent needed for the book.
Graph Decompositions
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Author : Reinhard Diestel
language : en
Publisher:
Release Date : 1990
Graph Decompositions written by Reinhard Diestel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Language Arts & Disciplines categories.
Graph Decompositions is the first book on a topic that belongs mainly to infinite graph theory. It offers a complete account of the theory of simplicial decompositions of graphs, from its origins in the 1930s right up to present-day research. In addition to being one of the most important tools in infinite graph theory, simplicial decompositions may be seen as a model for any kind of structural graph decomposition. The currently topical tree-decompositions, for example, have their origin in simplicial decompositions. The text is centred around a few guiding problems and concepts, such as the existence and the uniqueness problem of simplicial decompositions into primes, or the concept of excluded minors as a means of identifying a desired structure.It attempts to give as authentic a picture as possible of research in progress. To this end, it includes discussions of examples, proof strategies on the formation of new concepts, as well as numerous exercises and open problems. Graph Decompositions should prove attractive to any graph theorist or other mathematician interested in a new area of research, as well as to the advanced student looking for a lively and inspiring account of how such research evolves.
Introduction To Graph Theory
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Author : Gary Chartrand
language : en
Publisher: McGraw-Hill Science, Engineering & Mathematics
Release Date : 2005
Introduction To Graph Theory written by Gary Chartrand and has been published by McGraw-Hill Science, Engineering & Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Graph theory categories.
Economic applications of graphs ands equations, differnetiation rules for exponentiation of exponentials ...
Decompositions Of Graphs
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Author : Juraj Bosák
language : en
Publisher: Springer
Release Date : 1990-08-31
Decompositions Of Graphs written by Juraj Bosák and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-08-31 with Mathematics categories.
This nice text (twenty years in the writing, published posthumously) would serve well to introduce graduate students (those who can afford it ) to a rich and important class of graph-theoretic problems and concepts. Fifteen short chapters (under three broad topical heads), to each of which are attac