Methods Of Graph Decompositions
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Methods Of Graph Decompositions
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Author : DR VADIM. SKUMS ZVEROVICH (DR PAVEL.)
language : en
Publisher:
Release Date : 2024-06-15
Methods Of Graph Decompositions written by DR VADIM. SKUMS ZVEROVICH (DR PAVEL.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-15 with Mathematics categories.
This book discusses some methods of graph decompositions, which are highly instrumental when dealing with a number of fundamental problems of graph theory. The presented topics are united by the role played in their development by Professor Regina Tyshkevich, and the book is a tribute to her memory.
Graph Decompositions Theta Graphs And Related Graph Labelling Techniques
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Author : Andrew Blinco
language : en
Publisher:
Release Date : 2003
Graph Decompositions Theta Graphs And Related Graph Labelling Techniques written by Andrew Blinco and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Graph labelings categories.
The Theory Of 2 Structures
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Author : Andrzej Ehrenfeucht
language : en
Publisher: World Scientific
Release Date : 1999
The Theory Of 2 Structures written by Andrzej Ehrenfeucht and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 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 theoretical 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.
The Theory Of 2 Structures
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Author : A Ehrenfeucht
language : en
Publisher: World Scientific Publishing Company
Release Date : 1999-08-30
The Theory Of 2 Structures written by A 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. Request Inspection Copy
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: Oxford Science Publications
Release Date : 1990
Graph Decompositions written by Reinhard Diestel and has been published by Oxford Science Publications 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 ofresearch 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.
A Graph Decomposition Technique For Structuring Data
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Author : Paul A. Jensen
language : en
Publisher:
Release Date : 1967
A Graph Decomposition Technique For Structuring Data written by Paul A. Jensen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
For a number of advanced computer applications it will be necessary to store large quantities of data concerning relationships between a procedure for structuring transitive noncommutative relational data in a series of acyclical graphs which permit rapid access to the information. It is primarily concerned with providing algorithms which determine data structures which minimize the expected search time to discover the truth of the relation between an arbitrary pair of items. To provide computationally feasible techniques, it is necessary to temper the goal of optimality somewhat, using heuristic justification to greatly reduce the set of feasible structures. The resultant techniques utilize a max-flow min-cut algorithm and dynamic programming. (Author).
Linear Methods For Rational Triangle Decompositions
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Author : Kseniya Garaschuk
language : en
Publisher:
Release Date : 2014
Linear Methods For Rational Triangle Decompositions written by Kseniya Garaschuk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Given a graph G, a K3-decomposition of G, also called a triangle decomposition, is a set of subgraphs isomorphic to K3 whose edges partition the edge set of G. Further, a rational K_3-decomposition of G is a non-negative rational weighting of the copies of K3 in G such that the total weight on any edge of G equals one. In this thesis, we explore the problem of rational triangle decompositions of dense graphs. We start by considering necessary conditions for a rational triangle decomposition, which can be represented by facets of a convex cone generated by a certain incidence matrix. We identify several infinite families of these facets that represent meaningful obstructions to rational triangle decomposability of a graph. Further, we classify all facets on up to 9 vertices and check all 8-vertex graphs of degree at least four for rational triangle decomposability. As the study of graph decompositions is closely related to design theory, we also prove the existence of certain types of designs. We then explore sufficient conditions for rational triangle decomposability. A famous conjecture in the area due to Nash-Williams states that any sufficiently large graph (satisfying some divisibility conditions) with minimum degree at least 3/4v is K3-decomposable; the same conjecture stands for rational K3-decomposability (no divisibility conditions required). By perturbing and restricting the coverage matrix of a complete graph, we show that minimum degree of at least 22/23v is sufficient to guarantee that the given graph is rationally triangle decomposable. This density bound is a great improvement over the previously known results and is derived using estimates on the matrix norms and structures originating from association schemes.We also consider applications of rational triangle decompositions. The method we develop in the search for sufficient conditions provides an efficient way to generate certain sampling plans in statistical experimental design. Furthermore, rational graph decompositions serve as building blocks within certain design-theoretic proofs and we use them to prove that it is possible to complete partial designs given certain constraints.
Data Analysis Through Graph Decomposition
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Author : Marie Ely Piceno
language : en
Publisher:
Release Date : 2020
Data Analysis Through Graph Decomposition written by Marie Ely Piceno and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
This work is developed within the field of data mining and data visualization. Under the premise that many of the algorithms give as result huge amounts of data impossible to handle for the users, we work with the decomposition of Gaifman graphs and its variations as an option for data visualization. In fact, we apply the decomposition method based on the so-called 2-structures. This decomposition method has been theoretical developed but has not any practical application yet in this field, being this part of our contribution.Thus, from a dataset we construct the Gaifman graph (and possible variations of it) that represents information about co-occurrence patterns. More precisely, the construction of the Gaifman graphs from the dataset is based on co-occurrence, or lack of it, of items in the dataset. That is, those pair of items that appear together in any transaction are connected and those items that never appear together are disconnected. We may do the natural completion of the graph adding the absent edges with a different kind of edges, in this way we get a complete graph with two equivalence classes on its edges. Now, think of the graph where the kind of edges are determined by the multiplicity of the items that they connect, that is, by the number of transactions that contains the pair of items that the edge connects. In this case we have as many equivalence relations as different multiplicities, and we may apply some discretization methods on them to get different variations of the graphs.All these variations can be seen as 2-structures. The application of the 2-structure decomposition method produces as result a hierarchical visualization of the co-occurrences on data. In fact, the decomposition method is based on clan decomposition.Given a 2-structure defined on U, a set of vertices C, C subset of U, is a clan if, for each z not in C, z may not distinguish among the elements of C.We connect this decomposition with an associated closure space, developing this intuition by introducing a construction of implication sets, named clan implications.Based on the definition of a clan, let x, y be elements of any clan C, if there is z such that sees in a different way x and y, that is the edges (x,z) and (x,y) are in different equivalence classes, so z in C; this is equivalent to C logically entails the implication xy then z.Throughout the thesis, in order to explain our work in a constructive way, we first work with the case of having only two equivalence classes and its corresponding nomenclature (modules), and then we extend the theory to work with more equivalence classes. Our main contributions are: an algorithm (with its full implementation) for the clan decomposition method; the theorems that support our approach, and examples of its application to demonstrate its usability.
Complete Graph Decomposition Through Artistic Impressions Uum Press
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Author : Haslinda Ibrahim
language : en
Publisher: UUM Press
Release Date : 2021-03-01
Complete Graph Decomposition Through Artistic Impressions Uum Press written by Haslinda Ibrahim and has been published by UUM Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-01 with Education categories.
Complete Graph Decomposition through Artistic Impressions is a book that presents state-of-the-art of graph theory in resolving problems by graphical visualization. The book is unique in terms of the followings: • Each chapter begins with visual illustrations of ideas to represent (in pictures, figures etc.) and describe the problems that occur in the construction of algorithms. • The abstract concepts in graph theory are presented in a more relaxed and easily digestible form. • This book inspires readers to visualize hardcore mathematical concepts with a more meaningful and tangible story.