Conferenceseminar papers in all areas of graph theory will be published as a special issue. V super vertex magic labeling, we first look at some basic concepts and definitions of graph theory. The game is called sprouts and it is an invention of john horton conway. A labeling of a graph g is a mapping that carries graph elements to integers. He defined a graph to be magic if it has an edge labeling, within the range of real numbers, such that the sum of the labels around any vertex. If all the vertex weights respectively, edge weights have the same value then the labeling is called magic. Similarly if g has superior edge magic total labeling then, g k 1 admits edge bimagic total labeling. The notion of magic graph was first introduced by sunitha and vijaya kumar 4 in 1964. Magic labelings of graphs, symmetric magic squares citeseerx.
However, the problem remains open to find z k magic labeling for the inverse graphs from arbitrary groups. Any undefined graph theory terminology used in this papermaybe found in any textbook on graph theory, e. 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. Magic and antimagic graphs attributes, observations and. Applications of graph labeling in communication networks. Introduction to graceful graphs 2 acknowledgment i am deeply indebted to my late supervisor prof.
Amagic labeling lof p satisfying le 0 for all edges e ef is called a positive magic labeling. It is proved that every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one fig1. For a magic type of labeling in general, we require the sum of labels related to a vertex a vertex magic labeling or to an edge an edge magic labeling to be constant all over the graph. There are many kinds of graph labeling such as graceful labeling, magic labeling, prime labeling, and other different labeling techniques. In this paper, a generalization of a groupmagic graph is introduced and. If the weight is different for every vertex respectively, every edge then.
A bijection mapping that assigns natural numbers to vertices andor edges of a graph is called a labeling. Magic and antimagic labeling of graphs kiki ariyanti sugeng this thesis is submitted in total ful. Magic and antimagic labelings are among the oldest labeling schemes in graph theory. All graphs in this paper are finite, simple, planer and undirected. On the other hand, magic labelings were introduced by sedlacek in 1963 4. They conjecture that no tree has a super vertex magic total labeling. Let g v, e be a graph, where v and e represents the set of vertices and edges respectively. On antimagic labeling for graph products sciencedirect.
The paper was submitted to december 2014 by journal of graph theory. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called supermagic. Edge magic total labeling of g is assigning the labels to the vertices and edges, such that the sum of the labels of edge and its end vertices are constant k for each edge uv in g. Formally, given a graph g v, e, a vertex labelling is a function of v to a set of labels. A connected graph g is said to admit semi magic labeling, if the edges are labeled with integers such that for each vertex v the sum of the labels of all edges incident with v is same for all v.
Z, in other words it is a labeling of all edges by integers. A graph is said to be a fuzzy labeling graph if it has fuzzy labe ling. The concepts of fuzzy labeling and fuzzy magic labeling graph are introduced. We define a 1vertexmagic vertex labeling of a graph with v vertices as a bijection f taking the vertices to the integers 1, 2. Cn has super vertex magic total labeling if and only if n is odd, and no wheel, ladder, fan, friendship graph, complete bipartite graph or graph with a vertex of degree 1 has a super vertex magic total labeling. Further we prove that the wheel graph wn admits prime cordial labeling for n. It is of interest to note that h graph which is a 3 regular. The field of graph theory plays vital role in various fields. In general, all the graphs are not prime, it is very interesting to investigate graph families which admit prime labelling. Any undefined graph theory terminology used in this paper. 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. If the constraint is applied on only vertex set v then it is called vertex magic, if it is on the edge set e then it is called edge magic, if it is applied on both vertices and edges it leads to the total magic labeling. 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.
The application of fuzzy magic graph is illustrated with suitable example. He defined a graph to be magic if it has an edge labeling, within the range of real numbers, such that the. Labeling graph is a map from graph elements to numbers 2, in this paper we discuss about edge total magic labeling which domain is the set of all vertices and edges that map to the natural numbers. In this paper we investigate mean labeling of shadow graph of bistar and.
Some graphs with n edge magic labeling open access. A graph with such a function defined is called a vertexlabeled graph. In this work the domain of the labeling is the set of all vertices and edges which is always mapped to positive integers, i. On the degrees of a super vertex magic graph, discrete math. A magic labeling l of p satisfying le 0 for all edges e.
The notion of magic graph was first introduced by j. For all standard notation and terminology in graph theory we follow 4. By maintaining the order of the vertex and edge labelings and rotating them clockwise, an edge magic cycle graph can be created from a vertex magic cycle graph. The magic constants h and k are not necessarily equal. A graph is called anti magic if it admits an anti magic 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. If g is super edge magic graph then there exist bijective function g. In this paper we prove that the split graphs of k1,n and bn,n are prime cordial graphs. In this paper, we solve this problem and prove that all even degree regular graphs are antimagic. Math 215 project number 1 graph theory and the game. An edge magic labeling f of a graph with p vertices and q edges is a bijection. If n 0 mod 4, n 4, then kn has a super vertex magic total labeling.
Let a be any natural number then define a bijective function f. They conjecture that no tree has a super vertex magic total labeling and that k4n has a super vertex magic labeling when n 1. In the course of the problems we shall also work on writing proofs that use mathematical. Figure 2 shows just one way to create a vertex magic graph with three vertices.
A totally magic labeling is a labeling which is simultaneously both a vertex magic total labeling and an edge magic total labeling. The aim of journal of graph labeling is to bring together original and significant research articles in different areas of graph labeling and graph coloring. 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. Math 215 project number 1 graph theory and the game of sprouts this project introduces you to some aspects of graph theory via a game played by drawing graphs on a sheet of paper. An interesting open problem is whether it is possible to find.
Gallian, a dynamic survey of graph labeling, electr. The graph labeling problem that appears in graph theory. Introduction to graceful graphs 5 wn w is a wheel obtained from the cycle cn rn r is a crown with 2n edges hn h is a helm with 3n edges pn p is a path or snake of length n dn m d is a dragon obtained by joining the end point of path pm. Partially magic labelings the antimagicgraph conjecture. Zakariya, inverse graphs associated with finite groups, electronic journal of graph. 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 cycle. Magic labeling of disjoint union graphs springerlink. Based on the domain we distinguish vertex labelings, edge labelings and total labelings. Graph, graph labeling, edge labeling, edge magic labeling, 0edge magic labeling, 1 edge magic labeling.
Fuzzy bi magic labeling for the cycle graph and star graph are defined. G v, e, a unique natural number is called a labeling. There are numerous types of magic labelings in graph theory. Oct 15, 2019 in this paper, we show that if g is a supermagic even graph with a balanced edge coloring and m. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond. Magic labeling is a onetoone map that takes v g g e onto the integers from 1 with constant sumproperty. Sedlacek 9 introduced the concept of magic labeling. The objective of this paper is to introduce the concept of magic labeling in hesitancy fuzzy graph and finding results in hesitancy fuzzy graphs like path, cycle and star graphs by applying the. The concept of magic labeling in crisp graph was motivated by the notion of magic squares in number theory. Fibonacci mean anti magic labeling of circulant graph % 6 theorem 2.
Edgemagic labeling of some graphs research india publications. Many kinds of labelings have been studied and an excellent survey of graph labeling can be found in 3. In this paper the prime labeling of certain classes of graphs are discussed. Ringmagic labelings of graphs the australasian journal of. Whether all nonbipartite regular graphs of even degree are antimagic remained an open problem. 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. Magic and antimagic labeling of graphs kiki ariyanti.
Introduction 2 we generalize stanleys theorem theorem3. Fibonacci mean anti magic labeling on the given graph % j1,2. S, where the minimum is taken over all sets s for which the graph g admits an smagic labeling. Pdf hesitancy fuzzy magic labeling of simple graphs. If g is a dmagic even graph with a balanced edge coloring and n. Some researcher independently introduced the concepts of fuzzy graph theory by merging the fuzzy set and graph theory 9, 10. The graph g has the vertex set v g and edge set e g. 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. C n has a super vertex magic total labeling if and only if n is odd. He introduced me to the world of graph theory and was always patient, encouraging and resourceful.
They contain an introduction to basic concepts and results in graph theory, with a special emphasis put on the networktheoretic circuitcut dualism. In this chapter we study edge bimagic labeling, edge antimagic labeling and 1vertex bimagic vertex labeling. In this paper, a new concept of fuzzy bi magic labeling has been introduced. Petersen graph is a three regular graph with 10 vertices and 15 edges. If g is a magic graph and f is a magic labeling of g for which ther exists e eu such that fe1. 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. International journal for research in engineering application. A demonstration of the super edge magic labeling is as follows. Introduction a labeling of a graph g v, e is a mapping from the set of vertices, edges, or both vertices and edges to the set of labels.
If the labels are rotated clockwise, an edge magic graph is created with a magic number of 10. In particular a magic labeling on a graph with v vertices and e edges will be defined as a onetoone map taking the vertices and edges onto the integers 1, 2. A super edgemagic labeling of t6s2 figure 6 concluding observations we have obtained results similar to theorem 3. For many, this interplay is what makes graph theory so interesting. Graph, graph labeling, magic labeling, edge magic lab eling, vertex magic labeling, 0edgemagic labeling and 1edge magic labeling have b een discussed. Graph labeling is an important area of research in graph theory. Some graphs with n edge magic labeling neelam kumari 1, seema mehra 2 department of mathematics, m.
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. Yellen, graph theory and its applications, crc press, boca raton, 1999. Let h and k be the additive and multiplicative r magic values of an rring magic labeling f. 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. Magic and antimagic labeling of graphs researchgate. A graph g having a pendant vertex does not admits vsuper vertex magic labeling and esuper vertex magic labeling simentiously as in fig i and fig ii of example 2. In particular a magic labeling on a graph with v vertices and e edges. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph. Fuzzy magic labeling for some graphs like path, cycle, and star graph is defined. Pdf distance magic labelings of graphs semantic scholar. The z magic labeling on inverse graphs from finite cyclic group. This concise, selfcontained exposition is unique in its focus on the theory of magic graphs. Paper open access on super edgemagic total labeling of.
Esuper vertex magic labelings of graphs sciencedirect. The graphs which are considered in this paper are simple, finite, connected and undirected. There is a part of graph theory which actually deals with graphical drawing and presentation of graphs, brie. An antimagic 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. A helpful survey to know about numerous graph labeling is the one by j. In 2001, wallis introduced edge magic total labeling. In this paper a new labeling known as nedge magic labeling is introduced.
Results in this paper generalise some known results. In this paper we determine the distance magic index of trees and complete bipartite graphs. Qualitative labelings of graph elements have inspired research in diverse fields of human enquiry such as conflict resolution in social psychology. In 1996, edge magic labeling was rediscovered by ringel and llado. A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. We also show that the square graph of bn,n is a prime cordial graph while middle graph of pn is a prime cordial graph for n. A magic labeling of the graph g when t 3, using theorem 2. Introduction a graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. The concept of semi magic labeling was introduced by stewart. Likewise, an edge labelling is a function of to a set of labels. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called. A detailed survey about magic type labeling is given in the section 1. A super edge magic labeling of t6s2 figure 6 concluding observations we have obtained results similar to theorem 3. This paper addresses labeling graphs in such a way that the sum of the vertex labels and incident edge labels are the same for every vertex.
Graph labeling, vertex magic total labeling, vertex antimagic total labeling. Labeled graphs are becoming an increasingly useful family of mathematical models from abroad range of applications. Theory and applications labeled graphs are becoming an increasingly useful family of mathematical models for a broad range of applications. More generally, every graph each of whose vertexdegree is odd is z2magic. The concepts of graph labeling began about 50 years ago, and have been research topics for many mathematicians all over the world. Somasundaram and ponraj 4 have introduced the notion of mean labeling of graphs. Kotzig and rosa 10 define a magic labeling to be a total labeling in which the labels are. Graph labeling is currently an emerging area in the research of graph theory. For any magic labeling f of g,thereisaconstantcf such that for all edges.
In this thesis, we consider graph labelings that have weights associated with each edge andor vertex. Number theory, analytic geometry, fermats principle. The notes form the base text for the course mat62756 graph theory. A graph with such a labeling is an edge labeled graph. A vertex magic total vmt labeling of a graph g v,e is a bijection from the set of vertices and. Let r be a ring and g v,e be an rring magic graph of order p. Ring magic labelings of graphs 149 3 general results theorem 3. Pdf z kmagic labeling of some families of graphs researchgate. Friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic labeling are as follows. 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.
Depending upon the number of vertices and edges, a graph can be labeled in di. 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. Petersen graph admits fibonacci mean anti magic labeling. Some graphs with n edge magic labeling open access journals. A labeling of a graph g is a mapping that carries a set of graph elements, usually the vertices and edges into a set of numbers, usually integers. Labeling is the process of assigning integers to graph elements under some constraint. Fuzzy bimagic labeling on cycle graph and star graph.
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