In this paper, first we introduce an edge magic graceful labeling of a graph. This concise textbook is the only book of its kind in the. Download citation super edgemagic labelings of book graphs b n a graph g is called super edgemagic if there exists a bijection f from. Magic labeling on intervalvalued intuitionistic fuzzy graphs. The intriguing question is to decide which graphs are edge magic or vertex magic, or both. Graph labeling, edge magic labeling,total edge magic labeling, super edge magic labeling, complementary super edge magic labeling. Discover delightful childrens books with prime book box, a subscription that. 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. Further results on complementary super 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 includes updates on new research in the field. The graphs which are considered in this paper are simple, finite, connected and undirected. On complementary edge magic labeling ofcertain graphs.
This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond. A graph with such a labeling is an edge labeled graph. 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. This work aims to dispel certain longheld notions of a severe psychological disorder and a wellknown graph labeling conjecture. It is a graph consisting of triangles sharing a common edge. 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.
Does there exist a super edgemagic graph of order p,sizeq 2p5 and girth 5. If all the vertex weights respectively, edge weights have the same value then the labeling is called magic. Pdf distance magic labelings of graphs researchgate. Super edgemagic labelings of book graphs b n researchgate. A social role is a set of expectations we have about a behavior. We define a 1vertexmagic vertex labeling of a graph with v vertices as a bijection f taking the vertices to the integers 1, 2. This paper was written while the author was an undergraduate at elon university. 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. 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. Some of the major themes in graph theory are shown in figure 3. A p,q graph g v,e is said to be magic if there exist a bijection f.
In this paper we investigate the existence of super a, dedge antimagic total. We establish the existence of vertexmagic total labelings vmtls for several infinite classes of regular 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. Next we present some properties of super edge magic graceful graphs and prove. 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 genetics and linguistics, and from electrical engineering and geography to sociology and architecture. Francisco jose cano sevilla, the european mathematical society, april, 20.
A super edgemagic labeling of t6s2 figure 6 concluding observations we have obtained results similar to theorem 3. Diestel is excellent and has a free version available online. Super antimagicness of triangular book and diamond ladder graphs. Siam journal on discrete mathematics society for industrial. If there exist two constants k1 and k2 such that the above sum is either k1 or. Let h and k be the additive and multiplicative rmagic values of. In figure 3, it is shown a super edgemagic labeling of p 1 we ask the followings questions about the relation ordergirthsize. Fuzzy bimagic labeling for the cycle graph and star graph are defined. Ringmagic labelings of graphs 149 3 general results theorem 3. Formally, given a graph g v, e, a vertex labelling is a function of v to a set of labels. Partially magic labelings the antimagicgraph conjecture.
An example usage of graph theory in other scientific. Esuper vertex magic labelings of graphs sciencedirect. Magic and antimagic labelings are among the oldest labeling schemes in graph theory. If the weight is different for every vertex respectively, every edge then. 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. Two books dedicated to this topic, a very complete. Buy studies in graph theory magic labeling and related. After few years of zadehs milestone concept fuzzy sets theory, fuzzy graph theory developed as generliazation of graph theory by 2. The paper was submitted to december 2014 by journal of graph theory. The consecutively super edgemagic deficiency of graphs.
This concise, selfcontained exposition is unique in its focus on the theory of magic graphs. A bijection mapping that assigns natural numbers to vertices andor edges of a graph is called a labeling. If the book bn is super edgemagic with a super edgemagic labeling f. Labeling of 2regular graphs by even edge magic world scientific. Free graph theory books download ebooks online textbooks. This concise textbook is the only book of its kind in the area of magic graphs labeling, it contains numerous exercises, and their solutions, and. The edge magic strength of a graph g is denoted by emsg and is defined as the minimum of all constants where the minimum is taken over all edge magic labelings of g. Whether all nonbipartite regular graphs of even degree are antimagic remained an open problem. The place of super edgemagic labelings among other classes of. Friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic labeling are as follows. A labeling of a graph g is an assignment of mathematical objects to vertices, edges, or both vertices and edges subject to certain conditions.
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. Ring magic labelings of graphs 149 3 general results theorem 3. Buy studies in graph theory magic labeling and related concepts book online at best prices in india on. New constructions of edge bimagic graphs from magic graphs. A totally magic labeling is a labeling which is simultaneously both a vertexmagic total labeling and an edgemagic total labeling.
Labeling is the process of assigning integers to graph elements under some constraint. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called supermagic. 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 book magic graphs, is selfcontained, good, admirably clear, and a stimulating and very well written. Z, in other words it is a labeling of all edges by integers.
Most of these topics have been discussed in text books. Let r be a ring and g v,e be an rringmagic graph of order p. Introductory graph theory by gary chartrand, handbook of graphs and networks. Jun 30, 2016 after few years of zadehs milestone concept fuzzy sets theory, fuzzy graph theory developed as generliazation of graph theory by 2. Next we present some properties of super edge magic graceful graphs and prove some classes of graphs are super edge magic graceful. 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. Open problems involving super edgemagic labelings and. Graph labeling is one of the fascinating areas of graph theory with wide ranging applications. This book takes readers on a journey through these labelings, from early. 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. May 31, 2012 graph labeling is one of the fascinating areas of graph theory with wide ranging applications. The notation and terminology used in this paper are taken from gallian 9.
Let g be an undirected graph without loops or double connections between vertices. The magic constants h and k are not necessarily equal. A super edge magic labeling of t6s2 figure 6 concluding observations we have obtained results similar to theorem 3. If it is possible for a bipartite graph g, then we say that the minimum such number of isolated vertices is the consecutively super edgemagic deficiency of g. Some topics in graph theory the purpose of this book is to provide some results in a class of problems categorized as graph labeling. An enormous body of literature has grown around graph labeling in the last five decades. Magic graphs books pics download new books and magazines. To solve this problem, we introduce an edge magic graceful labeling of a graph. This concise, selfcontained exposition is unique in its focus on the theory of magic graphslabelings. We use the magic square of the order n to construct reverse super vertex magic labeling for kn. In this paper, a new concept of fuzzy bi magic labeling has been introduced. Let r be a ring and g v,e be an rring magic graph of order p. Magic and antimagic graphs attributes, observations and.
Finally, we demonstrate its performance by solving five open problems within the theory of magic graphs, posed in the book of. An edgemagic total labeling of a graph is a motivating research area. Studies in graph theory magic labeling and related concepts. In this thesis, we consider graph labelings that have weights associated with each edge andor vertex. One of the usages of graph theory is to give a uni. An edge magic labeling f of a graph with p vertices and q edges is a bijection f. Buy studies in graph theory magic labeling and related concepts.
In this paper, we solve this problem and prove that all even degree regular graphs are antimagic. Labeling theory concerns itself mostly not with the normal roles that define our lives, but with those very special roles that society provides for deviant behavior, called deviant roles, stigmatic roles, or social stigma. A graph with such a function defined is called a vertexlabeled graph. The 7page book graph of this type provides an example of a graph with no harmonious labeling. Sat and ip based algorithms for magic labeling with applications.
In this thesis, we consider graph labelings that have weights associated with each edge. Let h and k be the additive and multiplicative r magic values of an rring magic labeling f. Studies in graph theory magic labeling and related. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph.
This concise textbook 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. Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one fig1. A second type, which might be called a triangular book, is the complete tripartite graph k 1,1,p. Graph theory was introduced by leonhard euler in 1736 when he began dis. A graph g is called graceful if it has a graceful labeling. Fuzzy bimagic labeling on cycle graph and star graph. The main method of construction is to assemble a number of appropriately labeled copies of one graph into a single graph with a vmtl. In this paper, a new concept of fuzzy bimagic labeling has been introduced. Fuzzy bi magic labeling for the cycle graph and star graph are defined. On graceful labeling of some graphs with pendant edges. Intuitionistic fuzzy graph is a highly growing research area dealing with real life applications. We establish the existence of vertex magic total labelings vmtls for several infinite classes of regular graphs. It is not the easiest book around, but it runs deep and has a nice unifying theme of studying how. A graph g g v, e with v vertices is said to admit prime labeling, if its vertices can be labeled with distinct positive integers, not exceeding v such that the labels of each pair of.
1132 1627 248 1511 265 497 874 396 803 200 1562 326 911 1078 1592 660 1145 536 210 401 1392 1420 322 1346 1180 859 360 103 960 768 91 1192 803 871 117