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Magic And Antimagic Graphs
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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 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 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 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 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 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.
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 Fuzzy Graph Theory by : Sunil Mathew
Download or read book Fuzzy Graph Theory written by Sunil Mathew and published by Springer. This book was released on 2017-12-30 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine’s work on fuzzy interval graphs, fuzzy analogs of Marczewski’s theorem, and the Gilmore and Hoffman characterization. It also introduces them to the Fulkerson and Gross characterization and Menger’s theorem, the applications of which will be discussed in a forthcoming book by the same authors. This book also discusses in detail important concepts such as connectivity, distance and saturation in fuzzy graphs. Thanks to the good balance between the basics of fuzzy graph theory and new findings obtained by the authors, the book offers an excellent reference guide for advanced undergraduate and graduate students in mathematics, engineering and computer science, and an inspiring read for all researchers interested in new developments in fuzzy logic and applied mathematics.
Book Synopsis Recent Advancements in Graph Theory by : N. P. Shrimali
Download or read book Recent Advancements in Graph Theory written by N. P. Shrimali and published by CRC Press. This book was released on 2020-11-09 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory is a branch of discrete mathematics. It has many applications to many different areas of Science and Engineering. This book provides the most up-to-date research findings and applications in Graph Theory. This book focuses on the latest research in Graph Theory. It provides recent findings that are occurring in the field, offers insights on an international and transnational levels, identifies the gaps in the results, and includes forthcoming international studies and research, along with its applications in Networking, Computer Science, Chemistry, and Biological Sciences, etc. The book is written with researchers and post graduate students in mind.
Book Synopsis Proceedings of First International Conference on Mathematical Modeling and Computational Science by : Sheng-Lung Peng
Download or read book Proceedings of First International Conference on Mathematical Modeling and Computational Science written by Sheng-Lung Peng and published by Springer Nature. This book was released on 2021-05-04 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most recent scientific and technological advances in the fields of engineering mathematics and computational science, to strengthen the links in the scientific community. It is a collection of high-quality, peer-reviewed research papers presented at the First International Conference on Mathematical Modeling and Computational Science (ICMMCS 2020), held in Pattaya, Thailand, during 14–15 August 2020. The topics covered in the book are mathematical logic and foundations, numerical analysis, neural networks, fuzzy set theory, coding theory, higher algebra, number theory, graph theory and combinatory, computation in complex networks, calculus, differential educations and integration, application of soft computing, knowledge engineering, machine learning, artificial intelligence, big data and data analytics, high-performance computing, network and device security, and Internet of things (IoT).
Book Synopsis Strongly Antimagic Graphs by : Parker Le
Download or read book Strongly Antimagic Graphs written by Parker Le and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graph is a set of vertices, and edges which connect vertices. Given any graph G with m edges, we assign integers from 1 to m to the edges of G and consider vertex sums, the sums of the edge labels incident at each vertex. If there exists an assignment f: E(G) 6́2 {1, 2, . . . , m} for which the vertex sums are all distinct, then f is called an antimagic labeling for G. Further, such a labeling is called strongly antimagic for G if it satisfies the additional condition that: if a vertex u has fewer incident edges than the vertex v, then the vertex sum of u is strictly less than the vertex sum of v for any $u, v \\in V(G)$. Many graphs have been shown to be antimagic but have not been proved to be strongly antimagic. In this thesis, we prove that both trees (other than the 2-path) with at most one vertex of even degree, and the tree obtained from subdividing every edge into a 3-path, are strongly antimagic. Moreover, we investigate when the disjoint union of a cycle Cn with many copies of the 3-path are strongly antimagic. We show that there exists a number t = t(G) such that C4 8́® tP3 and C5 8́® tP3 are strongly antimagic for any t ♭́ư t(G).
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 Mathematics and Sports by : Joseph A. Gallian
Download or read book Mathematics and Sports written by Joseph A. Gallian and published by MAA. This book was released on 2010 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an eclectic compendium of the essays solicited for the 2010 Mathematics Awareness Month Web page on the theme of 'Mathematics and Sports'. In keeping with the goal of promoting mathematics awareness to a broad audience, all of the articles are accessible to university-level mathematics students and many are accessible to the general public. The book is divided into sections by the kind of sports. The section on American football includes an article that evaluates a method for reducing the advantage of the winner to a coin flip in an NFL overtime game; the section on track and field examines the ultimate limit on how fast a human can run 100 metres; the section on baseball includes an article on the likelihood of streaks; the section on golf has an article that describes the double-pendulum model of a golf swing and an article on modelling Tiger Woods' career.
Book Synopsis A Lifetime of Puzzles by : Erik D. Demaine
Download or read book A Lifetime of Puzzles written by Erik D. Demaine and published by CRC Press. This book was released on 2008-10-28 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler. And of course there is something from the original puzzlemaster himself, Martin Gardner.
Book Synopsis Computational Mathematics by : K. Thangavel
Download or read book Computational Mathematics written by K. Thangavel and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A review of computational design models and the most effective control mechanisms concerning physical phenomena, this book depicts a real-life system and emphasises the solution of a general class of inverse/design problems, presenting methodologies for dynamic coupling between experiments and computation.
Book Synopsis Information and Communication Technology for Competitive Strategies (ICTCS 2020) by : M. Shamim Kaiser
Download or read book Information and Communication Technology for Competitive Strategies (ICTCS 2020) written by M. Shamim Kaiser and published by Springer Nature. This book was released on 2021-07-05 with total page 1158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the best selected research papers presented at ICTCS 2020: Fifth International Conference on Information and Communication Technology for Competitive Strategies. The conference was held at Jaipur, Rajasthan, India during 11–12 December 2020. The book covers state-of-the-art as well as emerging topics pertaining to ICT and effective strategies for its implementation for engineering and managerial applications. This book contains papers mainly focused on ICT for computation, algorithms and data analytics and IT security.
Book Synopsis MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES), VOLUME 4, 2015 by : L. Mao
Download or read book MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES), VOLUME 4, 2015 written by L. Mao and published by Infinite Study. This book was released on with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers by many authors on subdivision of stars, Line digraph, cut vertex, Smarandachely k-domination number, Smarandachely transformation graph, Smarandachely super (a, d)-edge-antimagic total labeling, super (a, d)-EAT labeling, complete bipartite subdigraph, line cut vertex digraph, Smarandachely line cut vertex digraph and so on.
