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Magic Labelings Of Directed Graphs
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Download or read book Magic Graphs written by Alison M. Marr and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Magic squares are among the more popular mathematical recreations. Over the last 50 years, many generalizations of “magic” ideas have been applied to graphs. Recently there has been a resurgence of interest in “magic labelings” due to a number of results that have applications to the problem of decomposing graphs into trees. Key features of this second edition include: · a new chapter on magic labeling of directed graphs · applications of theorems from graph theory and interesting counting arguments · new research problems and exercises covering a range of difficulties · a fully updated bibliography and index This concise, self-contained exposition is unique in its focus on the theory of magic graphs/labelings. It may serve as a graduate or advanced undergraduate text for courses in mathematics or computer science, and as reference for the researcher.
Book Synopsis Magic Labelings of Directed Graphs by : Chedomir Angelo Barone
Download or read book Magic Labelings of Directed Graphs written by Chedomir Angelo Barone and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Let G be a directed graph with a total labeling. The additive arc-weight of an arc xy is the sum of the label on xy and the label on y. The additive directed vertex-weight of a vertex x is the sum of the label on x and the labels on all arcs with head at x. The graph is additive arc magic if all additive arc-weights are equal, and is additive directed vertex magic if all vertex-weights are equal. We provide a complete characterization of all graphs which permit an additive arc magic labeling. A complete characterization of all regular graphs which may be oriented to permit an additive directed vertex magic labeling is provided. The definition of the subtractive arc-weight of an arc xy is proposed, and a correspondence between graceful labelings and subtractive arc magic labelings is shown.
Book Synopsis Magic Labelings of Directed Graphs by :
Download or read book Magic Labelings of Directed Graphs written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Let G be a directed graph with a total labeling. The additive arc-weight of an arc xy is the sum of the label on xy and the label on y. The additive directed vertex-weight of a vertex x is the sum of the label on x and the labels on all arcs with head at x. The graph is additive arc magic if all additive arc-weights are equal, and is additive directed vertex magic if all vertex-weights are equal. We provide a complete characterization of all graphs which permit an additive arc magic labeling. A complete characterization of all regular graphs which may be oriented to permit an additive directed vertex magic labeling is provided. The definition of the subtractive arc-weight of an arc xy is proposed, and a correspondence between graceful labelings and subtractive arc magic labelings is shown.
Book Synopsis Magic and Antimagic Graphs by : Martin Bača
Download or read book Magic and Antimagic Graphs written by Martin Bača and published by Springer Nature. This book was released on 2019-09-14 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Magic and antimagic labelings are among the oldest labeling schemes in graph theory. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond. Starting from the very basics, the book offers a detailed account of all magic and antimagic type labelings of undirected graphs. Long-standing problems are surveyed and presented along with recent results in classical labelings. In addition, the book covers an assortment of variations on the labeling theme, all in one self-contained monograph. Assuming only basic familiarity with graphs, this book, complete with carefully written proofs of most results, is an ideal introduction to graph labeling for students learning the subject. More than 150 open problems and conjectures make it an invaluable guide for postgraduate and early career researchers, as well as an excellent reference for established graph theorists.
Book Synopsis Graceful, Harmonious and Magic Type Labelings by : Susana C. López
Download or read book Graceful, Harmonious and Magic Type Labelings written by Susana C. López and published by Springer. This book was released on 2017-02-26 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed toward upper undergraduate and graduate students in mathematics, this book examines the foremost forms of graph labelings including magic, harmonious, and graceful labelings. An overview of basic graph theory concepts and notation is provided along with the origins of graph labeling. Common methods and techniques are presented introducing readers to links between graph labels. A variety of useful techniques are presented to analyze and understand properties of graph labelings. The classical results integrated with new techniques, complete proofs, numerous exercises, and a variety of open problems, will provide readers with a solid understanding of graph labelings.
Book Synopsis Labelings of Directed Graphs by : Alison M. Marr
Download or read book Labelings of Directed Graphs written by Alison M. Marr and published by . This book was released on 2007 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation summarizes the main results in the area of graph labeling and introduces some new ideas for labelings of directed graphs. Graceful labelings of directed graphs are studied in depth. New results are given for certain orientations of paths, wheels, umbrellas, stars, and double stars. In addition, a new result on digraceful graphs is given for paths. Magic labelings of directed graphs are then introduced and some basic results are given. Finally, several other types of labelings on directed graphs are given and many questions for future work are posed.
Book Synopsis Pearls in Graph Theory by : Nora Hartsfield
Download or read book Pearls in Graph Theory written by Nora Hartsfield and published by Courier Corporation. This book was released on 2013-04-15 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stimulating and accessible, this undergraduate-level text covers basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.
Book Synopsis Super Edge-Antimagic Graphs by : Martin Baca
Download or read book Super Edge-Antimagic Graphs written by Martin Baca and published by Universal-Publishers. This book was released on 2008 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory, and graph labeling in particular, are fast-growing research areas in mathematics. New results are constantly being discovered and published at a rapidly increasing rate due to the enormous number of open problems and conjectures in the field. This book deals mainly with the super edge-antimagic branch of graph labeling. It is written for specialists, but could be read also by postgraduate or undergraduate students with high school knowledge of mathematics and a vibrant interest in problem-solving.
Book Synopsis An Atlas of Graphs by : Ronald C. Read
Download or read book An Atlas of Graphs written by Ronald C. Read and published by Mathematics. This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Distance Magic-type and Distance Antimagic-type Labelings of Graphs by :
Download or read book Distance Magic-type and Distance Antimagic-type Labelings of Graphs written by and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract : Generally speaking, a distance magic-type labeling of a graph G of order n is a bijection f from the vertex set of the graph to the first n natural numbers or to the elements of a group of order n, with the property that the weight of each vertex is the same. The weight of a vertex x is defined as the sum (or appropriate group operation) of all the labels of vertices adjacent to x. If instead we require that all weights differ, then we refer to the labeling as a distance antimagic-type labeling. This idea can be generalized for directed graphs; the weight will take into consideration the direction of the arcs. In this manuscript, we provide new results for d-handicap labeling, a distance antimagic-type labeling, and introduce a new distance magic-type labeling called orientable Gamma-distance magic labeling. A d-handicap distance antimagic labeling (or just d-handicap labeling for short) of a graph G=(V,E) of order n is a bijection f from V to {1,2,...,n} with induced weight function w(x_{i})=\underset{x_{j}\in N(x_{i})}{\sum}f(x_{j}) \] such that f(x_{i})=i and the sequence of weights w(x_{1}),w(x_{2}),...,w(x_{n}) forms an arithmetic sequence with constant difference d at least 1. If a graph G admits a d-handicap labeling, we say G is a d-handicap graph. A d-handicap incomplete tournament, H(n,k,d) is an incomplete tournament of n teams ranked with the first n natural numbers such that each team plays exactly k games and the strength of schedule of the ith ranked team is d more than the i+1st ranked team. That is, strength of schedule increases arithmetically with strength of team. Constructing an H(n,k,d) is equivalent to finding a d-handicap labeling of a k-regular graph of order n. In Chapter 2 we provide general constructions for every d at least 1 for large classes of both n and k, providing breadth and depth to the catalog of known H(n,k,d)'s. In Chapters 3 - 6, we introduce a new type of labeling called orientable Gamma-distance magic labeling. Let Gamma be an abelian group of order n. If for a graph G=(V,E) of order n there exists an orientation of G and a companion bijection f from V to Gamma with the property that there is an element mu in Gamma (called the magic constant) such that \[ w(x)=\sum_{y\in N_{G}^{+}(x)}\overrightarrow{f}(y)-\sum_{y\in N_{G}^{-}(x)}\overrightarrow{f}(y)=\mu for every x in V where w(x) is the weight of vertex x, we say that G is orientable Gamma-distance magic}. In addition to introducing the concept, we provide numerous results on orientable Z_n distance magic graphs, where Z_n is the cyclic group of order n. In Chapter 7, we summarize the results of this dissertation and provide suggestions for future work.
Book Synopsis Magic and Antimagic Labeling of Graphs by : Kiki Ariyanti Sugeng
Download or read book Magic and Antimagic Labeling of Graphs written by Kiki Ariyanti Sugeng and published by . This book was released on 2005 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling." --Abstract.
Book Synopsis Product of Digraphs, (super) Edge-magic Valences and Related Problems by : Prahu Mohan
Download or read book Product of Digraphs, (super) Edge-magic Valences and Related Problems written by Prahu Mohan and published by . This book was released on 2019 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete Mathematics, and in particular Graph Theory, has gained a lot of popularity during the last 7 decades. Among the many branches in Graph Theory, graph labelings has experimented a fast development, in particular during the last decade. One of the very important type of labelings are super edge-magic labelings introduced in 1998 by Enomoto et al. as a particular case of edge-magic labelings, introduced in 1970 by Kotzig and Rosa. An edge-magic labeling is a bijective mapping from the set of vertices and edges to [1,
Download or read book Magic Graphs written by W. D. Wallis and published by Birkhauser. This book was released on 2001 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Magic squares, their origins lost in antiquity, are among the more popular mathematical recreations. "Magic" ideas have also been applied to graphs, labellings, and trees. Unlike many elusive subjects in this area, the problem for vertex-magic total labelings has been solved, and the details are examined in this volume.
Book Synopsis Graphs & Digraphs, Fourth Edition by : Gary Chartrand
Download or read book Graphs & Digraphs, Fourth Edition written by Gary Chartrand and published by Chapman and Hall/CRC. This book was released on 1996-08-01 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third edition of the popular text on graph theory. As in previous editions, the text presents graph theory as a mathematical discipline and emphasizes clear exposition and well-written proofs. New in this edition are expanded treatments of graph decomposition and external graph theory, a study of graph vulnerability and domination, and introductions to voltage graphs, graph labelings, and the probabilistic method in graph theory.
Book Synopsis The Probabilistic Method by : Noga Alon
Download or read book The Probabilistic Method written by Noga Alon and published by John Wiley & Sons. This book was released on 2015-11-02 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.
Book Synopsis Handbook of Product Graphs by : Richard Hammack
Download or read book Handbook of Product Graphs written by Richard Hammack and published by CRC Press. This book was released on 2011-06-06 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, this second edition presents full proofs of many important results as well as up-to-date research and conjectures. It illustrates applications of graph products in several areas and contains well over 300 exercises. Supplementary material is available on the book's website.
Book Synopsis Handbook of Research on Advanced Applications of Graph Theory in Modern Society by : Pal, Madhumangal
Download or read book Handbook of Research on Advanced Applications of Graph Theory in Modern Society written by Pal, Madhumangal and published by IGI Global. This book was released on 2019-08-30 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the world of mathematics and computer science, technological advancements are constantly being researched and applied to ongoing issues. Setbacks in social networking, engineering, and automation are themes that affect everyday life, and researchers have been looking for new techniques in which to solve these challenges. Graph theory is a widely studied topic that is now being applied to real-life problems. The Handbook of Research on Advanced Applications of Graph Theory in Modern Society is an essential reference source that discusses recent developments on graph theory, as well as its representation in social networks, artificial neural networks, and many complex networks. The book aims to study results that are useful in the fields of robotics and machine learning and will examine different engineering issues that are closely related to fuzzy graph theory. Featuring research on topics such as artificial neural systems and robotics, this book is ideally designed for mathematicians, research scholars, practitioners, professionals, engineers, and students seeking an innovative overview of graphic theory.
