Download or read book A Study on Graph Labeling Problems written by J. Lisy Bennet and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory has applications in many areas of the computing, social and natural science. The theory is also intimately related to many branches of mathematics, including matrix theory, numerical analysis, probability, topology and combinatory. The fact is that graph theory serves as a mathematical for any system involving a binary relation.
Download or read book How to Label a Graph written by Gary Chartrand and published by Springer. This book was released on 2019-06-15 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book depicts graph labelings that have led to thought-provoking problems and conjectures. Problems and conjectures in graceful labelings, harmonious labelings, prime labelings, additive labelings, and zonal labelings are introduced with fundamentals, examples, and illustrations. A new labeling with a connection to the four color theorem is described to aid mathematicians to initiate new methods and techniques to study classical coloring problems from a new perspective. Researchers and graduate students interested in graph labelings will find the concepts and problems featured in this book valuable for finding new areas of research.
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.
Download or read book Graph Labeling and Non separating Trees written by Chenchu Bhaskar Gottipati and published by . This book was released on 2014 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies two independent problems, one is about graph labeling and the other problem is related to connectivity condition in a simple graph. Graph labeling is a rapidly developing area of research in graph theory, having connections with a variety of application-oriented areas such as VLSI optimization, data structures and data representation. Furthermore, the connectivity conditions in a simple graphs may help us to study the new aspects of ad hoc networks, social networks and web graphs. In chapter 2, we study path systems, reduced path systems and how to construct a super edge-graceful tree with any number of edges using path systems. First, we give an algorithm to reduce a labeled path system to a smaller labeled path system of a dierent type. First, we investigate the cases (m; k) = (3; 5) and (m; k) = (4; 7), where m is the number of paths and 2k is the length of each path, and then we give a generalization for any k;m = 3 and m = 4. We also describe a procedure to construct a super-edge-graceful tree with any number of edges. In chapter 3, we study connected graphs with certain distance-degree condition and find characteristics of a subtree of the graph whose deletion does not disconnect the graph. If T is a tree on n vertices, n > 3, and if G is a connected graph such that d (u) + d (v) + d (u; v) > 2n for every pair of distinct vertices of G, it has been conjectured that G must have a non-separating copy of T. We prove a result for the special case in which d (u)+d (v)+d (u; v) > 2n+2 for every pair of distinct vertices of G, and improve this slightly for trees of diameter at least four and for some trees of diameter three. In chapter 4, we characterize the graphs on at most 8 vertices with d (u) + d (v) + d (u; v) > 7 for every pair of distinct vertices of G, and no non-separating copy of K1;3. we also study several algorithms used to verify Locke's conjecture for a special case of non-separating trees of size k in any connected 2k-cohesive graph up to 9 vertices.
Download or read book Graph Theory written by S. B. Rao and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: GRAPH THEORY: Research Directions, contains ten articles, mainly survey type, on some current research areas in Graph Theory, namely, graceful labeling, L(2,1)-labelling, complexity of graph labeling problems, dominations, interval graphs, matrices and graphs, colouring of labelled graphs and hypergraphs, self-complementary graphs, and strongly regular graphs. Several research problems have been mentioned in the book and at the end of each article a number of references have been included. This book will be beneficial for researchers and useful for beginners who want to do research in these topics.
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.
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.
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 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.
Download or read book The graph labeling model and its application to the problem of edge linking written by University of Michigan. Computing Research Laboratory and published by . This book was released on 1983 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Studies in Graph Algorithms generation and Labeling Problems written by Shmuel Zaks and published by . This book was released on 1979 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graph Theory and Computing written by Ronald C. Read and published by Academic Press. This book was released on 2014-05-12 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory and Computing focuses on the processes, methodologies, problems, and approaches involved in graph theory and computer science. The book first elaborates on alternating chain methods, average height of planted plane trees, and numbering of a graph. Discussions focus on numbered graphs and difference sets, Euclidean models and complete graphs, classes and conditions for graceful graphs, and maximum matching problem. The manuscript then elaborates on the evolution of the path number of a graph, production of graphs by computer, and graph-theoretic programming language. Topics include FORTRAN characteristics of GTPL, design considerations, representation and identification of graphs in a computer, production of simple graphs and star topologies, and production of stars having a given topology. The manuscript examines the entropy of transformed finite-state automata and associated languages; counting hexagonal and triangular polyominoes; and symmetry of cubical and general polyominoes. Graph coloring algorithms, algebraic isomorphism invariants for graphs of automata, and coding of various kinds of unlabeled trees are also discussed. The publication is a valuable source of information for researchers interested in graph theory and computing.
Download or read book Labelings of Discrete Structures and Applications written by B. D. Acharya and published by Narosa Publishing House. This book was released on 2007-12-21 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems arising from the study of a variety of labeling schemes of the elements of any discrete structure such as a graph, a directed graph, a hypergraph or a signed graph is a potential area of research with a lots of challenging unsolved problems. Research papers giving recent developments and directions for further research on topics such as graceful labelings, graph decomposition, multiplicative labelings, set labelings, sigma graphs, orthogonal labelings, Skolem and Hooked Skolem graceful labelings for graphs and signed graphs, set magic labeling, k- equitable graphs and Arithmetic graphs by leading experts in the respective fields are included in this volume. This volume will serve as an excellent reference for experts and research scholars working on Graph Labeling Problems.
Download or read book MATHEMATICAL COMBINATORICS INTERNATIONAL BOOK SERIES written by Linfan MAO and published by Infinite Study. This book was released on with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. TheMathematical Combinatorics (International Book Series) is a fully refereed international book series with an ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandachemulti-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.
Download or read book Graph Labeling Problems with Distance Conditions written by Ellen Panofsky and published by . This book was released on 2008 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: A proper channel assignment on a weighted graph G = (V, E, w) where V is the vertex set, E is the edge set, and w is a function assigning positive integer weights to the edges in E, is a function c : V & rarr; {lcub}0, 1 ..., k{rcub} such that c(u) -- c(v) & ge; w (uv) for all edges uv in E. The goal of the channel assignment problem on G is to find the smallest number k such that there exists a proper channel assignment whose maximum value is k. A specific type of channel assignment problem is the L(2,1) problem. The L(2,1) problem looks at a graph G = (V, E), and tries to find a proper L(2,1) coloring function c : V & rarr; {lcub}0, 1 ..., k{rcub} such that c(u) -- c (v) & ge; 2 if uv is an edge in G and c(u) -- c(v) & ge; 1 if the shortest path connecting u and v has length two. The goal of the L(2,1) problem on G is to find the smallest number k, such that there exists a proper L(2,1) coloring whose maximum value is k. The minimum number k is called the L(2,1) number, and is denoted lambda2,1 (G). This problem was originally posed by Jerrold Griggs and Roger Yeh in 1992. They conjectured that for every graph G, lambda 2,1(G) & le; Delta2 where Delta is the maximum degree of G. We first look at some basic techniques that will be used throughout the thesis. We then prove that if the Griggs/Yeh conjecture can be shown for bipartite graphs then lambda2,1 (G) & le; Delta 2 + 1 for all comparability graphs G. We also show that the Giggs/Yeh conjecture is true for permutation graphs with Delta = 3, 4 and all AT-free graphs. We then begin looking at graphs with maximum degree three, and show that it is sufficient to show the Griggs/Yeh conjecture on the class of maximum degree three graphs without certain induced subgraphs. Looking at this special class of graphs, we explore a special structure that yields a partial L(2,1) coloring. This partial coloring leads to another interesting coloring problem known as the list channel assignment problem (and list L(2,1) problem).
Download or read book External Labeling written by Michael A. Bekos and published by Springer Nature. This book was released on 2022-06-01 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focusses on techniques for automating the procedure of creating external labelings, also known as callout labelings. In this labeling type, the features within an illustration are connected by thin leader lines (called leaders) with their labels, which are placed in the empty space surrounding the image. In general, textual labels describing graphical features in maps, technical illustrations (such as assembly instructions or cutaway illustrations), or anatomy drawings are an important aspect of visualization that convey information on the objects of the visualization and help the reader understand what is being displayed. Most labeling techniques can be classified into two main categories depending on the "distance" of the labels to their associated features. Internal labels are placed inside or in the direct neighborhood of features, while external labels, which form the topic of this book, are placed in the margins outside the illustration, where they do not occlude the illustration itself. Both approaches form well-studied topics in diverse areas of computer science with several important milestones. The goal of this book is twofold. The first is to serve as an entry point for the interested reader who wants to get familiar with the basic concepts of external labeling, as it introduces a unified and extensible taxonomy of labeling models suitable for a wide range of applications. The second is to serve as a point of reference for more experienced people in the field, as it brings forth a comprehensive overview of a wide range of approaches to produce external labelings that are efficient either in terms of different algorithmic optimization criteria or in terms of their usability in specific application domains. The book mostly concentrates on algorithmic aspects of external labeling, but it also presents various visual aspects that affect the aesthetic quality and usability of external labeling.
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.
