Depending upon the number of vertices and edges, a graph can be labeled in di. On edge magic total labeling of 7, 3cycle books hindawi. On the degrees of a super vertex magic graph, discrete math. Buy studies in graph theory magic labeling and related concepts book online at best prices in india on.
Magic graphs books pics download new books and magazines. Howard saul beckers book outsiders was extremely influential in the development of this theory and its rise to popularity. The 7page book graph of this type provides an example of a graph with no harmonious labeling. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called supermagic. Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one fig1. A graph with such a function defined is called a vertexlabeled graph. This work aims to dispel certain longheld notions of a severe psychological disorder and a wellknown graph labeling conjecture. Applications of graph labeling in communication networks.
Degreemagic labelings on the join and composition of. Magic and antimagic graphs attributes, observations and. We define a 1vertex magic vertex labeling of a graph with v vertices as a bijection f taking the vertices to the integers 1, 2. W d wallis magic squares are among the more popular mathematical recreations. Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph g is called esuper vertex magic if it admits a esuper vertex magic labeling. The book magic graphs, is selfcontained, good, admirably clear, and a stimulating and very well written. A totally magic labeling is a labeling which is simultaneously both a vertexmagic total labeling and an edgemagic total labeling. A totally magic injection with deficiency 0 is called a totally magic labeling. Friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic labeling are as follows. If a 2regular graph is avertex consecutive magic, then n is odd and a.
A bijection mapping that assigns natural numbers to vertices andor edges of a graph is called a labeling. Pdf the study of labeling graphs exposed to various distance constraints is motivated by the problem of minimizing the span of. Buy studies in graph theory magic labeling and related concepts. For graph theoretic terminology, we refer to harary 2. In the mathematical discipline of graph theory, a graph labelling is the assignment of labels, traditionally represented by integers, to edges andor vertices of a graph. Studies in graph theory magic labeling and related concepts. A graph consists of some points and lines between them. Some topics in graph theory the purpose of this book is to provide some results in a class of problems categorized as graph labeling. In the mathematical discipline of graph theory, a graph labelling is the assignment of labels, traditionally represented by integers, to edges andor vertices of a graph formally, given a graph, a vertex labelling is a function of to a set of labels.
Pdf edge trimagic total labeling of mobios ladder, book and. Let r be a ring and g v,e be an rringmagic graph of order p. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond. Pdf distance magic labelings of graphs researchgate. Magic graphs alison m marr, w d wallis bok 9780817683900. In this thesis, we consider graph labelings that have weights associated with each edge andor vertex. May 28, 2015 whether all nonbipartite regular graphs of even degree are antimagic remained an open problem. Formally, given a graph g v, e, a vertex labelling is a function of v to a set of labels. Kotzig and rosa 1970 introduced the concept of total edgemagic labeling. In general, all the graphs are not prime, it is very interesting to investigate graph families which admit prime labelling. In section 4 we show that the windmill w r, k is crmagic, thus providing a family of crmagic graphs. An interesting open problem is whether it is possible to find a super edgemagic labeling for a general merge graph tm sn for m 2, n 1. Labeling, magic labeling, edge magic total labeling, even edge magic total labeling 2010 mathematics subject classification.
This concise text book is the only book of its kind in the area of magic graphslabeling, it contains numerous exercises, and their solutions, and includes updates on new research in the field. An interesting open problem is whether it is possible to find a super edge magic labeling for a general merge graph tm sn for m 2, n 1. Two edge magic f 1 and f 2 of g are equivalent if f 1 f 2 or f 1. Likewise, an edge labelling is a function of to a set of labels.
Let g be super edgemagic labeling graph and f be a super edgemagic labeling of g. The paper was submitted to december 2014 by journal of graph theory. Aimed toward upper undergraduate and graduate students in mathematics, this book examines the foremost forms of graph labelings including magic, harmonious, and graceful labelings. Over the last 50 years, many generalizations of magic ideas have been applied to graphs. Buy studies in graph theory magic labeling and related. For instance there is the labeling theory that corresponds to homosexuality. The 7page book graph of this type provides an example of a graph with no harmonious labeling a second type, which might be called a triangular book, is the complete. This concise text book is the only book of its kind in the area of magic graphs labeling, it contains numerous exercises, and their solutions, and includes updates on new research in the field. Magic labelings on cycles and wheels university of guelph. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called.
In this paper, we solve two research problems from the book magic. Square difference labeling, square difference graph. This paper provides insights into some aspects of the possibilities and role of mind, consciousness, and their relation to mathematical logic with the application of problem solving in the fields of psychology and graph theory. One of the important areas in graph theory is graph labeling used in many applications like coding theory, xray crystallography, radar, astronomy, circuit design, communication network addressing, data base management. Pdf fuzzy magic labeling of simple graphs researchgate. An hmagic graph g is said to be hzerosum or just zerosum if there is a magic labeling of g in zh that induces a vertex labeling with sum 0. The dual of an avertex consecutive magic total labeling for a regular graph is an a. In this paper, we study some of the basic properties of e super vertex magic graphs and also prove the existence or nonexistence of e super vertex magic labeling for some families of graphs. In this paper, we solve this problem and prove that all even degree regular graphs are antimagic. If such a labeling exists, then magic constant k is called valence of f and g is said to be edge magic graph. This concise textbook is the only book of its kind in the area of magic graphslabeling, it contains numerous exercises, and their solutions, and.
An edgemagic total labeling of a graph is a motivating research area. Studies in graph theory magic labeling and related. The place of super edgemagic labelings among other classes of. Magic and antimagic labeling of graphs kiki ariyanti sugeng. Nov 06, 2012 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. An example usage of graph theory in other scientific fields. Clearly, a graph that has an edge pendant is not zerosum. Discrete mathematics graph theory labeled graphs magic labeling it is conjectured that every tree with edges whose nodes are all trivalent or monovalent can be given a magic labeling such that the integers 1, 2. Graph labeling is one of the fascinating areas of graph theory with wide ranging applications. Let h and k be the additive and multiplicative rmagic values of. Introduction all graphs in this paper are simple finite undirected and nontrivial graph gv, e with vertex set v and the edge set e. Graph, function, bijection, dragon, mobius ladder, book, trimagic labeling.
A total edge magic labeling of a graph with n vertices and m edges is a bijection f from v u e to the integers 1, 2. This monograph deals with a particular class of graph labeling problems. That is, it is a cartesian product of a star and a single edge. If the book bn is super edgemagic with a super edgemagic labeling f. The crossreferences in the text and in the margins are active links. W d wallis this book is a good guide for graduate students beginning research in graph labelings. One kind, which may be called a quadrilateral book, consists of p quadrilaterals sharing a common edge known as the spine or base of the book.
It is a graph consisting of triangles sharing a common edge. They contain an introduction to basic concepts and results in graph theory, with a special emphasis put on the networktheoretic circuitcut dualism. A second type, which might be called a triangular book, is the complete tripartite graph k 1,1,p. Ringmagic labelings of graphs 149 3 general results theorem 3. Super magic and arithmetic labelings of the graphs p. Given a graph, the goal is to assign numbers to all edges and vertices of the graph in such a way as to satisfy certain constraints. Magic and antimagic labelings are among the oldest labeling schemes in graph theory. The notes form the base text for the course mat62756 graph theory. Labeling theory was developed by sociologists during the 1960s.
Graceful, harmonious and magic type labelings overdrive. A super edge magic labeling of t6s2 figure 6 concluding observations we have obtained results similar to theorem 3. This concise, selfcontained exposition is unique in its focus on the theory of magic graphs. A super edgemagic labeling of t6s2 figure 6 concluding observations we have obtained results similar to theorem 3. 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.
Labeling theory is also connected to other fields besides crime. Siam journal on discrete mathematics siam society for. The length of the lines and position of the points do not matter. Yellen, graph theory and its applications, crc press, boca raton, 1999. Let g be an undirected graph without loops or double connections between vertices. Z, in other words it is a labeling of all edges by integers. If the labels are rotated clockwise, an edgemagic graph is created with a magic number of 10.
On complementary edge magic labeling ofcertain graphs. The field of graph theory plays vital role in various fields. Some of the major themes in graph theory are shown in figure 3. The main campus is located three miles from the atlantic ocean, on an 850acre site. Kotzig and rosa 1970 introduced the concept of total edge magic labeling. An enormous body of literature has grown around graph labeling in the last five decades. Magic and antimagic labeling of graphs researchgate. Starting from the very basics, the book offers a detailed account of all magic and antimagic type labelings of undirected. Umbrella graph, p nqs n graph, c nq sn graphs are square difference graphs. Graph labelings were first introduced in the 1960s where the vertices and edges are assigned real values or subsets of a set subject to certain conditions.
Esuper vertex magic labelings of graphs sciencedirect. The magic constants h and k are not necessarily equal. If the weight is different for every vertex respectively, every edge then. A graph is called vertex magic if a labeling using those same numbers exists so that for each vertex v, the sum of the label of v and of all edges adjacent to v is equal to a constant k. An overview of basic graph theory concepts and notation is provided along with the origins of graph labeling. This book takes readers on a journey through these labelings, from early. Introduction graph theory is used in different fields like chemistry,social sciences, computer sciences and operations research. In an edge magic total labeling, the constraint is that the sum of the numbers attached to each edge and its vertices be the same for all. Further, sunitha and vijaya k umar 17 proposed the notion of.
Most of these topics have been discussed in text books. Figure 2 shows just one way to create a vertexmagic graph with three vertices. Totally magic labelings of graphs the australasian journal of. Labeling of 2regular graphs by even edge magic world scientific. If all the vertex weights respectively, edge weights have the same value then the labeling is called magic. An example usage of graph theory in other scientific. The intriguing question is to decide which graphs are edge magic or vertex magic, or both.
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