On Sets And Graphs
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On Sets And Graphs
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Author : Eugenio G. Omodeo
language : en
Publisher: Springer
Release Date : 2017-05-11
On Sets And Graphs written by Eugenio G. Omodeo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-11 with Computers categories.
This treatise presents an integrated perspective on the interplay of set theory and graph theory, providing an extensive selection of examples that highlight how methods from one theory can be used to better solve problems originated in the other. Features: explores the interrelationships between sets and graphs and their applications to finite combinatorics; introduces the fundamental graph-theoretical notions from the standpoint of both set theory and dyadic logic, and presents a discussion on set universes; explains how sets can conveniently model graphs, discussing set graphs and set-theoretic representations of claw-free graphs; investigates when it is convenient to represent sets by graphs, covering counting and encoding problems, the random generation of sets, and the analysis of infinite sets; presents excerpts of formal proofs concerning graphs, whose correctness was verified by means of an automated proof-assistant; contains numerous exercises, examples, definitions, problems and insight panels.
More Sets Graphs And Numbers
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Author : Ervin Gyori
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-02
More Sets Graphs And Numbers written by Ervin Gyori 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 2010-10-02 with Mathematics categories.
This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers are sure to inspire further research.
Graphs And Order
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Author : Ivan Rival
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Graphs And Order written by Ivan Rival 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.
This volume contains the accounts of the principal survey papers presented at GRAPHS and ORDER, held at Banff, Canada from May 18 to May 31, 1984. This conference was supported by grants from the N.A.T.O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the University of Calgary. We are grateful for all of this considerable support. Almost fifty years ago the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. On that occasion the principal lectures were delivered by G. Birkhoff, O. Ore and M.H. Stone. In those days the theory of ordered sets was thought to be a vigorous relative of group theory. Some twenty-five years ago the Symposium on Partially Ordered Sets and Lattice Theory was held in Monterey, U.S.A. Among the principal speakers at that meeting were R.P. Dilworth, B. Jonsson, A. Tarski and G. Birkhoff. Lattice theory had turned inward: it was concerned primarily with problems about lattices themselves. As a matter of fact the problems that were then posed have, by now, in many instances, been completely solved.
Hypergraphs
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Author : C. Berge
language : en
Publisher: Elsevier
Release Date : 1984-05-01
Hypergraphs written by C. Berge and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-05-01 with Mathematics categories.
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.
Sets Graphs And Numbers
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Author : Vera T. Sós
language : en
Publisher: North Holland
Release Date : 1992
Sets Graphs And Numbers written by Vera T. Sós and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Theory And Application Of Graphs
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Author : Junming Xu
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-31
Theory And Application Of Graphs written by Junming Xu 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 2003-07-31 with Mathematics categories.
In the spectrum of mathematics, graph theory which studies a mathe matical structure on a set of elements with a binary relation, as a recognized discipline, is a relative newcomer. In recent three decades the exciting and rapidly growing area of the subject abounds with new mathematical devel opments and significant applications to real-world problems. More and more colleges and universities have made it a required course for the senior or the beginning postgraduate students who are majoring in mathematics, computer science, electronics, scientific management and others. This book provides an introduction to graph theory for these students. The richness of theory and the wideness of applications make it impossi ble to include all topics in graph theory in a textbook for one semester. All materials presented in this book, however, I believe, are the most classical, fundamental, interesting and important. The method we deal with the mate rials is to particularly lay stress on digraphs, regarding undirected graphs as their special cases. My own experience from teaching out of the subject more than ten years at University of Science and Technology of China (USTC) shows that this treatment makes hardly the course di:fficult, but much more accords with the essence and the development trend of the subject.
Distances And Domination In Graphs
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Author : Ismael González Yero
language : en
Publisher: MDPI
Release Date : 2020-11-18
Distances And Domination In Graphs written by Ismael González Yero and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-18 with Mathematics categories.
This book presents a compendium of the 10 articles published in the recent Special Issue “Distance and Domination in Graphs”. The works appearing herein deal with several topics on graph theory that relate to the metric and dominating properties of graphs. The topics of the gathered publications deal with some new open lines of investigations that cover not only graphs, but also digraphs. Different variations in dominating sets or resolving sets are appearing, and a review on some networks’ curvatures is also present.
Fundamentals Of Domination In Graphs
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Author : Teresa W. Haynes
language : en
Publisher: CRC Press
Release Date : 2013-12-16
Fundamentals Of Domination In Graphs written by Teresa W. Haynes and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-16 with Mathematics categories.
"Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination."
Graph Representation Learning
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Author : William L. William L. Hamilton
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Graph Representation Learning written by William L. William L. Hamilton and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Computers categories.
Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
Research Trends In Graph Theory And Applications
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Author : Daniela Ferrero
language : en
Publisher: Springer Nature
Release Date : 2021-09-06
Research Trends In Graph Theory And Applications written by Daniela Ferrero and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-06 with Mathematics categories.
The Workshop for Women in Graph Theory and Applications was held at the Institute for Mathematics and Its Applications (University of Minnesota, Minneapolis) on August 19-23, 2019. During this five-day workshop, 42 participants performed collaborative research, in six teams, each focused on open problems in different areas of graph theory and its applications. The research work of each team was led by two experts in the corresponding area, who prior to the workshop, carefully selected relevant and meaningful open problems that would yield high-quality research and results of strong impact. As a result, all six teams have made significant contributions to several open problems in their respective areas. The workshop led to the creation of the Women in Graph Theory and Applications Research Collaboration Network, which provided the framework to continue collaborating and to produce this volume. This book contains six chapters, each of them on one of the different areas of research at the Workshop for Women in Graph Theory and Applications, and written by participants of each team.