The ncm graph is edgemagic for m3 and n 2, 3, proof. Fuzzy magic labeling for some graphs like path, cycle, and star graph is defined. We also show that some graphs admits e super vertex magic labeling and v super vertex magic labeling simentiously but some not 1, 2, 3, 6. Whether all nonbipartite regular graphs of even degree are antimagic remained an open problem. A graph is called anti magic if it admits an anti magic labeling. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one. A comprehensive introduction by nora hartsfield and gerhard ringel. Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to practical problems. We defined fuzzy bi magic labeling for cycle and star graph. Labeling of a graph g is an assignment of labels to vertices or edges or both following certain rules, a useful survey on graph labeling by j. This work aims to dispel certain longheld notions of a severe psychological disorder and a wellknown graph labeling conjecture. In this chapter we study edge bimagic labeling, edge antimagic labeling and 1vertex bimagic vertex labeling.
On the degrees of a super vertex magic graph, discrete math. May 31, 2012 graph labeling is one of the fascinating areas of graph theory with wide ranging applications. If the book bn is super edgemagic with a super edgemagic labeling f such that. Let r be a ring and g v,e be an rring magic graph of order p. The ncm graph is edge magic for m3 and n 2, 3 example. A detailed survey about magic type labeling is given in the section 1. An overview of basic graph theory concepts and notation is provided along with the origins of graph labeling. The least integer k for which a graph g has a lucky labeling from the set 1,2,k is the lucky number of g, denoted by.
Pdf on antimagic labeling for graph products researchgate. 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. On antimagic labeling for graph products sciencedirect. There are numerous types of magic labelings in graph theory.
Formally, given a graph g v, e, a vertex labelling is a function of v to a set of labels. Quick tour of linear algebra and graph theory basic linear algebra adjacency matrix the adjacency matrix m of a graph is the matrix such that mi. In this paper the prime labeling of certain classes of graphs are discussed. It is total magic if its edges and vertices can be labelled so that the vertex label plus the sum of labels on edges incident with that vertex is a constant. Graph theory is the study of mathematical structures called graphs. In this paper, we solve this problem and prove that all even degree regular graphs are antimagic. Studies in graph theory magic labeling and related. An example usage of graph theory in other scientific. We define a graph as a pair v, e, where v is a nonempty set, and. It is proved that every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. Graceful, harmonious and magic type labelings relations. General definitions of cycles, wheels, fans, friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic labeling are as follows. Magic and antimagic labeling of graphs researchgate. It took a hundred years before the second important contribution of kirchhoff 9 had been made for the analysis of electrical networks.
If g is a d magic even graph with a balanced edge coloring and n. Let h and k be the additive and multiplicative r magic values of an rring magic labeling f. After few years of zadehs milestone concept fuzzy sets theory, fuzzy graph theory developed as generliazation of graph theory by 2. A graph is vertex magic if its vertices can be labelled so that the sum on any edge is the same. On graceful labeling of some graphs with pendant edges. Introduction all graphs in this paper are simple finite undirected and nontrivial graph gv, e with vertex set v and the edge set e. A vertex magic total vmt labeling of a graph g v,e is a bijection from the set of vertices and. Show that if every component of a graph is bipartite, then the graph is bipartite. It focuses on the linguistic tendency of majorities to negatively label minorities or those seen as deviant from norms.
Most of these topics have been discussed in text books. Preface enumerative combinatorics has undergone enormous development since the publication of the. For all standard notation and terminology in graph theory we follow 4. The paper was submitted to december 2014 by journal of graph theory. There are a great many variations on the concept of magic labelling of a graph. Z, in other words it is a labeling of all edges by integers. A bijection mapping that assigns natural numbers to vertices andor edges of a graph is called a labeling. Ringmagic labelings of graphs australasian journal of. Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one fig1. This concise, selfcontained exposition is unique in its focus on the theory of magic graphs. The reverse super vertex magic labeling of a graph is the reverse vertex magic labeling with the condition that all the vertices of the graph takes the labels 1,2,3, v. 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. Baskoro, and rinovia simanjuntak, total vertex irregularity strength of trees with maximum degree five, elec. Research in graph theory has lead to one of the important area called labeling of graphs.
Cycle is a graph where there is an edge between the adjacent. A general reference for graph theoretic notations is 3. Graph labeling is currently an emerging area in the research of graph theory. Magic and antimagic labelings are among the oldest labeling schemes in graph theory. Reinhard diestel graph theory electronic edition 2000 c springerverlag new york 1997, 2000 this is an electronic version of the second 2000 edition of the above springer book, from their series graduate texts in mathematics, vol. Then the graph g is cmagic if there exists a total labelling f. A graph g is called esuper vertex magic if it admits a esuper vertex magic labeling.
If n 0 mod 4, n 4, then kn has a super vertex magic total labeling. Esuper vertex magic labelings of graphs sciencedirect. Graph, graph labeling, magic labeling, edge magic lab eling, vertex magic labeling, 0edgemagic labeling and 1edge magic labeling have b een discussed. The concepts of fuzzy labeling and fuzzy magic labeling graph are introduced. As a natural extension of previously defined graph labelings, we introduce in this paper a new magic labeling whose evaluation is based on the neighbourhood of a vertex. This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. V super vertex magic labeling, we first look at some basic concepts and definitions of graph theory. Appendix graph theory terminology 655 first edition numbering 658 list of notation 670 index 5.
Pdf an antimagic labeling of a finite simple undirected graph with p. Applications of graph labeling in communication networks. Aimed toward upper undergraduate and graduate students in mathematics, this book examines the foremost forms of graph labelings including magic, harmonious, and graceful labelings. It is not the easiest book around, but it runs deep and has a nice unifying theme of studying how.
Thus, the book can also be used by students pursuing research work in phd programs. Free graph theory books download ebooks online textbooks. Introduction graph theory is used in different fields like chemistry,social sciences, computer sciences and operations research. The application of fuzzy magic graph is illustrated with suitable example. An anti magic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the set of integers 1, 2, q such that the vertex sums are pairwise distinct, where the vertex sum at one vertex is the sum of labels of all edges incident to such vertex. Introductory graph theory by gary chartrand, handbook of graphs and networks. Magic labeling of disjoint union graphs springerlink.
For graph theoretic terminology, we refer to harary 2. The ncm graphs have edge magic labeling for m3 and n 2, 3 as shown below. Pdf distance magic labelings of graphs semantic scholar. Magic labeling, vertex magic total labeling, edge total magic labeling, total magic labeling, cycles, wheels, fan, friendship graphs. Prove that a complete graph with nvertices contains nn 12 edges. If the weight is different for every vertex respectively, every edge then we called the labeling antimagic. Theory and applications graph labelings, where the vertices and edges are assigned, real values subject to certain conditions, have often been motivated by their utility to various applied fields and their intrinsic mathematical interest logico mathematical. The overflow blog how the pandemic changed traffic trends from 400m visitors across 172 stack. A graph is known as graceful when its vertices are labeled from 0 to v, the size of the graph, and this labelling induces an edge labelling from 1 to e. Introduction the graphs we have considered here are finite, simple and undirected. The dots are called nodes or vertices and the lines are called edges. E be a simple, undirected and nite graph with p vertices and q edges. Graph theory experienced a tremendous growth in the 20th century.
Fuzzy bimagic labeling on cycle graph and star graph. The perception of labeling to the vertices and edges in graphs has flourished with types of labeling being applied in different areas by the researchers. It is of interest to note that h graph which is a 3 regular. As a result, a wealth of new models was invented so as to capture these properties. The book includes number of quasiindependent topics. Buy studies in graph theory magic labeling and related. Further we investigated the properties of such labeling on these graphs. F or all standard notation and terminology in graph theory we. A super edge magic labeling of t6s2 figure 6 concluding observations we have obtained results similar to theorem 3.
Let g be a graph with vertex set v and edge set e, where v. 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. There are different types of labeling such as graceful labeling, magic labeling, edgegraceful labeling, prime labeling, radio labeling, harmonious labeling etc. As a research area, graph theory is still relatively young, but it is maturing rapidly with many deep results having been discovered over the last couple of decades. The 7page book graph of this type provides an example of a graph with no harmonious labeling. We have shown that the removal of a fuzzy bridge from a fuzzy magic cycle with odd nodes reduces the strength of a fuzzy magic. In this paper, we introduce the concept of fuzzy bi magic labeling in graphs. Graceful labeling for corona and flower graph aip publishing. Graph labeling is one of the fascinating areas of graph theory with wide ranging applications. Square difference labeling, square difference graph. It has become more clear what are the essential topics. In particular a magic labeling on a graph with v vertices and e edges will be defined as a one. Studies in graph theory magic labeling and related concepts. Friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic labeling are as follows.
Prove that a nite graph is bipartite if and only if it contains no cycles of odd length. For any magic labeling f of g,thereisaconstantcf such that for all edges. Some topics in graph theory the purpose of this book is to provide some results in a class of problems categorized as graph labeling. For all other terminology and notations we follows harary harary 1972. A graph with such a function defined is called a vertexlabeled graph. A graph is called antimagic if it admits an antimagic labeling. A graph g is called graceful if it has a graceful labeling.
The notes form the base text for the course mat62756 graph theory. In this paper, we show that if g is a supermagic even graph with a balanced edge coloring and m. There are many kinds of graph labeling such as graceful labeling, magic labeling, prime labeling, and other different labeling techniques. This monograph is a complete account of magic and antimagic graph labelings.
Grid paper notebook, quad ruled, 100 sheets large, 8. One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science. 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. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph. For any edge e, the label of e is the positive difference between the two vertices incident with e.
A graph is vertexmagic if its vertices can be labelled so that the sum on any edge is the same. In this thesis, we consider graph labelings that have weights associated with each edge andor vertex. 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. Graph labeling is an important area of research in graph theory. For standard terminology and notation in graph theory we follow harary 1. It is the number of edges connected coming in or leaving out, for the graphs in given images we cannot differentiate which edge is coming in and which one is going out to a vertex. Ring magic labelings of graphs 149 3 general results theorem 3. Another important open problem to look into is, whether there exists an edge magic labeling for a general ncm graph for m3 and 0 mar 09, 2015 graph 1 has 5 edges, graph 2 has 3 edges, graph 3 has 0 edges and graph 4 has 4 edges. A difference labeling of g is an injection f from v to the set of non. The ncm graphs have edgemagic labeling for m3 and n 2, 3 as shown below. Pdf z kmagic labeling of some families of graphs researchgate. 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.
Graph labeling is one of the most growing areas in graph theory. 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. The concept of distance magic labeling of a graph was motivated by the. A graph labeling is an assignment of integers to the vertices or edges, or both. Some of the major themes in graph theory are shown in figure 3. An enormous body of literature has grown around graph labeling in the last five decades. Discover delightful childrens books with prime book box, a subscription that. Dec 11, 2009 labeling theory holds that deviance is not a quality of the act because it is the result of personality factors associated with committing deviance. Hartsfield and ringel conjectured in 1990 that all connected graphs except k 2 are antimagic. In this thesis, we explore polynomials concerning two main streams in graph theory, that is, graph labelings and graph colorings. Labeling, magic labeling, edge magic total labeling, even edge magic total labeling 2010 mathematics subject classification. A graph with such a labeling is an edge labeled graph. Kotzig and rosa 5, for example, defined a magic labeling to be a labeling. Magic and antimagic graphs attributes, observations and.
The labeling of the vertices respectively edges is injective if distinct vertices respectively edges have distinct labels. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond. In a weighted graph, the weight of a path is the sum of the weights of the edges traversed. The field of graph theory plays vital role in various fields. 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. If the weight is different for every vertex respectively, every edge then. If all the vertex weights respectively, edge weights have the same value then the labeling is called magic. Every fuzzy magic graph is a fuzzy labeling graph,but the converse is not true. Immersion and embedding of 2regular digraphs, flows in bidirected graphs, average degree of graph powers, classical graph properties and graph parameters and their definability in sol, algebraic and modeltheoretic methods in. I used this book to teach a course this semester, the students liked it and it is a very good book indeed.
Prove that if uis a vertex of odd degree in a graph, then there exists a path from uto another. We use the magic square of the order n to construct reverse super vertex magic labeling for kn. Ngurah and rinovia simanjuntak, on the super edge magic deficiency of join product and chain graphs, electron. Results in this paper generalise some known results. The place of super edgemagic labelings among other classes of. They contain an introduction to basic concepts and results in graph theory, with a special emphasis put on the networktheoretic circuitcut dualism. It is a graph consisting of triangles sharing a common edge. Diestel is excellent and has a free version available online. Degrees of any pair of vertices in magic fuzzy graph always different from each others and sum of degrees of nodes must be equal to twice the membership values of all arcs. What are some good books for selfstudying graph theory. Umbrella graph, p nqs n graph, c nq sn graphs are square difference graphs.
The crossreferences in the text and in the margins are active links. Starting from the very basics, the book offers a detailed account of all magic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. Browse other questions tagged binatorics graphtheory primenumbers graphcolorings applications or ask your own question. In 1967, rosa 46 introduced graph labelings or what he has called valuations in.
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