On Sets And Graphs

Author : Eugenio G. Omodeo,Alberto Policriti,Alexandru I. Tomescu
Publisher : Springer
Page : 275 pages
File Size : 40,5 Mb
Release : 2017-05-11
Category : Computers
ISBN : 9783319549811

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On Sets and Graphs by Eugenio G. Omodeo,Alberto Policriti,Alexandru I. Tomescu Pdf

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.

Author : William L. William L. Hamilton
Publisher : Springer Nature
Page : 141 pages
File Size : 48,5 Mb
Release : 2022-06-01
Category : Computers
ISBN : 9783031015885

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Graph Representation Learning by William L. William L. Hamilton Pdf

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.

Author : Ivan Rival
Publisher : Springer Science & Business Media
Page : 798 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400953154

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Graphs and Order by Ivan Rival Pdf

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.

Author : Gunther Schmidt,Thomas Ströhlein
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642779688

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Relations and Graphs by Gunther Schmidt,Thomas Ströhlein Pdf

Relational methods can be found at various places in computer science, notably in data base theory, relational semantics of concurrency, relationaltype theory, analysis of rewriting systems, and modern programming language design. In addition, they appear in algorithms analysis and in the bulk of discrete mathematics taught to computer scientists. This book is devoted to the background of these methods. It explains how to use relational and graph-theoretic methods systematically in computer science. A powerful formal framework of relational algebra is developed with respect to applications to a diverse range of problem areas. Results are first motivated by practical examples, often visualized by both Boolean 0-1-matrices and graphs, and then derived algebraically.

Author : Junming Xu
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 45,5 Mb
Release : 2003-07-31
Category : Mathematics
ISBN : 1402075405

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Theory and Application of Graphs by Junming Xu Pdf

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.

Author : Richard J. Trudeau
Publisher : Courier Corporation
Page : 224 pages
File Size : 49,8 Mb
Release : 2013-04-15
Category : Mathematics
ISBN : 9780486318660

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Introduction to Graph Theory by Richard J. Trudeau Pdf

Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.

Author : Ervin Gyori,Gyula O.H. Katona,László Lovász
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 52,9 Mb
Release : 2010-10-02
Category : Mathematics
ISBN : 9783540324393

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More Sets, Graphs and Numbers by Ervin Gyori,Gyula O.H. Katona,László Lovász Pdf

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.

Author : I. M. Gelfand,E. G. Glagoleva,E. E. Shnol
Publisher : Courier Corporation
Page : 112 pages
File Size : 40,9 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780486317137

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Functions and Graphs by I. M. Gelfand,E. G. Glagoleva,E. E. Shnol Pdf

This text demonstrates the fundamentals of graph theory. The 1st part employs simple functions to analyze basics; 2nd half deals with linear functions, quadratic trinomials, linear fractional functions, power functions, rational functions. 1969 edition.

Author : David Avis,Alain Hertz,Odile Marcotte
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 45,6 Mb
Release : 2005-12-06
Category : Business & Economics
ISBN : 9780387255927

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Graph Theory and Combinatorial Optimization by David Avis,Alain Hertz,Odile Marcotte Pdf

Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem. Graph Theory and Combinatorial Optimization explores the field's classical foundations and its developing theories, ideas and applications to new problems. The book examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application. The field's leading researchers have contributed chapters in their areas of expertise.

Author : George Osipenko
Publisher : Springer
Page : 288 pages
File Size : 53,6 Mb
Release : 2006-10-28
Category : Mathematics
ISBN : 9783540355953

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Dynamical Systems, Graphs, and Algorithms by George Osipenko Pdf

This book describes a family of algorithms for studying the global structure of systems. By a finite covering of the phase space we construct a directed graph with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used, among other things, to locate the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, and more.

Author : Alan Frieze,Michał Karoński
Publisher : Cambridge University Press
Page : 483 pages
File Size : 43,6 Mb
Release : 2016
Category : Mathematics
ISBN : 9781107118508

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Introduction to Random Graphs by Alan Frieze,Michał Karoński Pdf

The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Author : Domenico Cantone,Eugenio Omodeo,Alberto Policriti
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 42,5 Mb
Release : 2013-06-29
Category : Computers
ISBN : 9781475734522

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Set Theory for Computing by Domenico Cantone,Eugenio Omodeo,Alberto Policriti Pdf

An up-to-date and comprehensive account of set-oriented symbolic manipulation and automated reasoning methods. This book is of interest to graduates and researchers in theoretical computer science and computational logic and automated reasoning.

Author : Vera T. Sós,A. Hajnal
Publisher : North Holland
Page : 760 pages
File Size : 45,6 Mb
Release : 1992
Category : Mathematics
ISBN : UOM:39015029448142

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Sets, Graphs and Numbers by Vera T. Sós,A. Hajnal Pdf

Author : Edward R. Scheinerman,Daniel H. Ullman
Publisher : Courier Corporation
Page : 240 pages
File Size : 46,6 Mb
Release : 2013-04-29
Category : Mathematics
ISBN : 9780486292137

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Fractional Graph Theory by Edward R. Scheinerman,Daniel H. Ullman Pdf

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.

Author : TeresaW. Haynes
Publisher : Routledge
Page : 519 pages
File Size : 42,8 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351454643

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Domination in Graphs by TeresaW. Haynes Pdf

""Presents the latest in graph domination by leading researchers from around the world-furnishing known results, open research problems, and proof techniques. Maintains standardized terminology and notation throughout for greater accessibility. Covers recent developments in domination in graphs and digraphs, dominating functions, combinatorial problems on chessboards, and more.