Likewise, an edge labelling is a function of to a set of labels. We define a 1vertexmagic vertex labeling of a graph with v vertices as a bijection f taking the vertices to the integers 1, 2. A graph is called supermagic if there is a labeling of edges, where all edges are differently labeled with consecutive positive integers such that the sum of the labels of all edges, which are incident to each vertex of this graph, is a constant. 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. This concise, selfcontained exposition is unique in its focus on the theory of magic graphs. Graph labeling is one of the fascinating areas of graph theory with wide ranging applications. Friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic labeling are as follows.
Studies in graph theory magic labeling and related. Pdf edge trimagic total labeling of mobios ladder, book and. Some topics in graph theory the purpose of this book is to provide some results in a class of problems categorized as graph labeling. The intriguing question is to decide which graphs are edge magic or vertex magic, or both. Umbrella graph, p nqs n graph, c nq sn graphs are square difference graphs. Magic labelings on cycles and wheels university of guelph. A graph with such a function defined is called a vertexlabeled graph. A totally magic labeling is a labeling which is simultaneously both a vertexmagic total labeling and an edgemagic total labeling. Esuper vertex magic labelings of graphs sciencedirect. Formally, given a graph g v, e, a vertex labelling is a function of v to a set of labels.
Magic and antimagic labeling of graphs researchgate. A second type, which might be called a triangular book, is the complete tripartite graph k 1,1,p. Buy studies in graph theory magic labeling and related concepts book online at best prices in india on. Graceful, harmonious and magic type labelings overdrive. Most of these topics have been discussed in text books. Kotzig and rosa 1970 introduced the concept of total edgemagic labeling. 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. The notes form the base text for the course mat62756 graph theory. In this paper, we solve this problem and prove that all even degree regular graphs are antimagic.
Let g be an undirected graph without loops or double connections between vertices. That is, it is a cartesian product of a star and a single edge. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called supermagic. The magic constants h and k are not necessarily equal. Graph, function, bijection, dragon, mobius ladder, book, trimagic labeling. A totally magic injection with deficiency 0 is called a totally magic labeling. For graph theoretic terminology, we refer to harary 2. A super edgemagic labeling of t6s2 figure 6 concluding observations we have obtained results similar to theorem 3. Totally magic labelings of graphs the australasian journal of.
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. Siam journal on discrete mathematics siam society for. W d wallis magic squares are among the more popular mathematical recreations. Some of the major themes in graph theory are shown in figure 3. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph.
The 7page book graph of this type provides an example of a graph with no harmonious labeling. A super edge magic labeling of t6s2 figure 6 concluding observations we have obtained results similar to theorem 3. Applications of graph labeling in communication networks. If all the vertex weights respectively, edge weights have the same value then the labeling is called magic. Labeling theory was developed by sociologists during the 1960s. Labeling theory is also connected to other fields besides crime. Pdf distance magic labelings of graphs researchgate. If a 2regular graph is avertex consecutive magic, then n is odd and a. On complementary edge magic labeling ofcertain graphs. 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. If the book bn is super edgemagic with a super edgemagic labeling f. Magic and antimagic labelings are among the oldest labeling schemes in graph theory. 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.
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. They contain an introduction to basic concepts and results in graph theory, with a special emphasis put on the networktheoretic circuitcut dualism. A graph g is called esuper vertex magic if it admits a esuper vertex magic labeling. An example usage of graph theory in other scientific. A graph with such a labeling is an edge labeled graph. It is a graph consisting of triangles sharing a common edge. 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. Introduction all graphs in this paper are simple finite undirected and nontrivial graph gv, e with vertex set v and the edge set e.
Super magic and arithmetic labelings of the graphs p. 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. Studies in graph theory magic labeling and related concepts. 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 edgemagic labeling for a general merge graph tm sn for m 2, n 1. The length of the lines and position of the points do not matter. Over the last 50 years, many generalizations of magic ideas have been applied to graphs. Z, in other words it is a labeling of all edges by integers. Figure 2 shows just one way to create a vertexmagic graph with three vertices. In section 4 we show that the windmill w r, k is crmagic, thus providing a family of crmagic graphs. Let g be super edgemagic labeling graph and f be a super edgemagic labeling of g. Magic graphs alison m marr, w d wallis bok 9780817683900. This book takes readers on a journey through these labelings, from early. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond.
If the labels are rotated clockwise, an edgemagic graph is created with a magic number of 10. Two edge magic f 1 and f 2 of g are equivalent if f 1 f 2 or f 1. In this thesis, we consider graph labelings that have weights associated with each edge andor vertex. An overview of basic graph theory concepts and notation is provided along with the origins of graph labeling. Further, sunitha and vijaya k umar 17 proposed the notion of. In this paper, we solve two research problems from the book magic. For instance there is the labeling theory that corresponds to homosexuality.
Magic and antimagic graphs attributes, observations and. Buy studies in graph theory magic labeling and related concepts. The main campus is located three miles from the atlantic ocean, on an 850acre site. Magic graphs books pics download new books and magazines. 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. A bijection mapping that assigns natural numbers to vertices andor edges of a graph is called a labeling. The book magic graphs, is selfcontained, good, admirably clear, and a stimulating and very well written. Labeling of 2regular graphs by even edge magic world scientific. The field of graph theory plays vital role in various fields. Starting from the very basics, the book offers a detailed account of all magic and antimagic type labelings of undirected. Depending upon the number of vertices and edges, a graph can be labeled in di. Ringmagic labelings of graphs 149 3 general results theorem 3. Pdf fuzzy magic labeling of simple graphs researchgate.
On edge magic total labeling of 7, 3cycle books hindawi. The paper was submitted to december 2014 by journal of graph theory. This work aims to dispel certain longheld notions of a severe psychological disorder and a wellknown graph labeling conjecture. Introduction graph theory is used in different fields like chemistry,social sciences, computer sciences and operations research. If the weight is different for every vertex respectively, every edge then. The place of super edgemagic labelings among other classes of. 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.
An enormous body of literature has grown around graph labeling in the last five decades. 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. Labeling, magic labeling, edge magic total labeling, even edge magic total labeling 2010 mathematics subject classification. Aimed toward upper undergraduate and graduate students in mathematics, this book examines the foremost forms of graph labelings including magic, harmonious, and graceful labelings. Graph labeling is one of the most growing areas in graph theory. This monograph deals with a particular class of graph labeling problems. 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. 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. Degreemagic labelings on the join and composition of.
Yellen, graph theory and its applications, crc press, boca raton, 1999. The crossreferences in the text and in the margins are active links. A graph consists of some points and lines between them. 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. 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. Square difference labeling, square difference graph. Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one fig1. If such a labeling exists, then magic constant k is called valence of f and g is said to be edge magic graph. On the degrees of a super vertex magic graph, discrete math. Let h and k be the additive and multiplicative rmagic values of. Let r be a ring and g v,e be an rringmagic graph of order p. An example usage of graph theory in other scientific fields. The dual of an avertex consecutive magic total labeling for a regular graph is an a. Clearly, a graph that has an edge pendant is not zerosum.
Buy studies in graph theory magic labeling and related. 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. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called. Pdf the study of labeling graphs exposed to various distance constraints is motivated by the problem of minimizing the span of. Kotzig and rosa 1970 introduced the concept of total edge magic labeling. Howard saul beckers book outsiders was extremely influential in the development of this theory and its rise to popularity. 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. May 28, 2015 whether all nonbipartite regular graphs of even degree are antimagic remained an open problem. 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. In general, all the graphs are not prime, it is very interesting to investigate graph families which admit prime labelling. W d wallis this book is a good guide for graduate students beginning research in graph labelings. Magic and antimagic labeling of graphs kiki ariyanti sugeng.
1625 48 486 1162 1235 1370 1582 281 879 1571 1253 221 970 779 139 148 209 1336 132 207 31 1466 376 1201 270 1313 542 241