An effort has been made to present the various topics in the theory of graphs. It may seem strange to term a graph as having an \antimagic labeling, but the term comes from its connection to magic labelings and magic squares. We will discuss only a certain few important types of graphs in this chapter. Graph theory is one of the branches of modern mathematics having experienced a most impressive development in recent years. Jenzy and trenkler 4 proved that a graph g is magic if and only if every edge of g is contained in a 12factor. Does there exist a walk crossing each of the seven. An introduction to enumeration and graph theory bona, miklos this is a textbook for an introductory combinatorics course lasting one or two semesters. In recent years, graph theory has established itself as an important mathematical tool in a wide variety of subjects, ranging from operational research and chemistry to. Example in the above graph, there are three vertices named a, b, and c. The inhouse pdf rendering service has been withdrawn. A total edge magic graph is called a super edge magic if fvg 1,2. This book is a comprehensive text on graph theory and the subject matter is presented in an organized and.
Degreemagic graphs extend supermagic regular graphs. Also a graph g which admits a super edge magic graceful labeling is called a super edge magic graceful graph. Graph theory on demand printing of 02787 by frank harary. Raziya begam tree with three vertices and s2 a star on three vertices then t3 s2 is formed as follows. Graph theory 121 circuit a circuit is a path that begins and ends at the same vertex. It is not the easiest book around, but it runs deep and has a nice unifying theme of studying how.
Acknowledgement much of the material in these notes is from the books graph theory by reinhard diestel and introductiontographtheory bydouglaswest. An amagic graph g is said to be z kmagic graph if the group a is z k, the group of integers modulo k and these graphs are referred as kmagic graphs. Graph theory wikibooks, open books for an open world. For the love of physics walter lewin may 16, 2011 duration. Graph theory 3 a graph is a diagram of points and lines connected to the points. An edge magic graceful labeling of a graph g is super edge magic graceful if the set of vertex labels is 1, 2, p. Any graph which admits a distance magic labeling is called a distance magic graph. Connected a graph is connected if there is a path from any vertex. The basis of graph theory is in combinatorics, and the role of graphics is. Starting from the very basics, the book offers a detailed account of all magic and antimagic type labelings of undirected graphs. A graph consists of some points and lines between them. Null graph a graph having no edges is called a null graph. Modular decomposition and cographs, separating cliques and chordal graphs, bipartite graphs, trees, graph width parameters, perfect graph theorem and related results, properties of almost all graphs, extremal graph theory, ramseys theorem with variations, minors and minor closed graph classes. Magic graph is a powerful and easytouse graphing tool for plotting and analysing graphs of mathematical functions.
Two important graphs connected to the group action. Degreemagic labelings on the join and composition of. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond. Let g be an avertex consecutive magic graph of n vertices and e n. Graph theoretic applications and models usually involve connections to the real. Magic squares are among the more popular mathematical recreations. In this paper we present a survey of existing results on distance magic graphs along with our recent results,open. This is a very basic survey on magic labelings of graphs, which are a special case of the general topic of graph labelings. Diestel is excellent and has a free version available online. In addition, the book covers an assortment of variations on the labeling theme, all in one selfcontained monograph. There is nothing in the book that would not be accessible for an undergraduate. Looking for avertex consecutive magic graphs with e n and minimum degree one, we show the following result. The fascinating world of graph theory explores the questions and puzzles that have been studied, and often solved, through graph theory.
The dots are called nodes or vertices and the lines are. One reason graph theory is such a rich area of study is that it deals with such a fundamental concept. An introduction to enumeration and graph theory pdf a walk through combinatorics. 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. It has at least one line joining a set of two vertices with no vertex connecting itself. General definitions of cycles, wheels, fans, friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic labeling are as follows. A circuit starting and ending at vertex a is shown below.
Longstanding problems are surveyed and presented along with recent results in classical labelings. Contents list of figuresv using these notesxi chapter 1. In an undirected graph, an edge is an unordered pair of vertices. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the. A magic graph is a graph whose edges are labelled by positive integers, so that the sum over the edges incident with any vertex is the same, independent of the choice of vertex. In this paper, the necessary and sufficient conditions for the existence of degreemagic labelings of graphs obtained by taking the join and.
The fundamental domain of the action is a subgraph x of such that x. Graph is a mathematical representation of a network and it describes the relationship between lines and points. Magic and antimagic labelings are among the oldest labeling schemes in graph theory. Graph theory is the study of interactions between nodes vertices and edges connections between the vertices, and it relates to topics such as combinatorics, scheduling, and connectivity making it useful. The problem of identifying which kinds of super edge magic graphs are weak magic graphs is addressed in this paper. Muntanerbatle, on edgemagic labelings of certain disjoint union graphs, j. Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one. In these algorithms, data structure issues have a large role, too see e. Over the last 50 years, many generalizations of magic ideas have been applied to graphs. Zmagic graphs were considered by stanley 18, 19, who pointed out that the theory of magic.
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