An edge magic graceful labeling of a graph g is super edge magic graceful if the set of vertex labels is 1, 2, p. An element of the edge set is a twoelement subset of the vertex set. Magic and antimagic labeling of graphs kiki ariyanti sugeng this thesis is submitted in total ful. The game is called sprouts and it is an invention of john horton conway. Magic squares can trace their origin back to ancient china somewhere around the 7th century bce 4. We also study directed graphs or digraphs d v,e, where the edges have a direction, that is, the edges are ordered. Murty, graph theory with applications, macmillan, lon. An edge e or ordered pair is a connection between two nodes u,v. Department of mathematics, university of manitoba, winnipeg, manitoba. A connected graph on 2 n vertices is defined to be xormagic if the vertices can be labeled with distinct nbit binary numbers in such a way that the label at each vertex is equal to the bitwise xor of the labels on the adjacent vertices. Graph theory 121 circuit a circuit is a path that begins and ends at the same vertex. The concept of graphs in graph theory stands up on some basic terms such as point, line, vertex, edge, degree of vertices, properties of graphs, etc.
A graph is a finite set of vertices and edges where every edge connects two vertices. Differential geometry in graphs harvard university. A typical directed graph this graph can be represented by a matrix m, called the adjacency matrix, as shown below. The intriguing question is to decide which graphs are edge magic or vertex magic, or both. For graph theory notations and terminology not described in this paper, the readers are referred to 1. General definitions of cycles, wheels, fans, friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic labeling are as follows. Raziya begam tree with three vertices and s2 a star on three vertices then t3 s2 is formed as follows. Also, jgj jvgjdenotes the number of verticesandeg jegjdenotesthenumberofedges. The length of the lines and position of the points do not matter. The question about the existence of such valuations arises from. If g gv,e is a graph, then vg is a finite non empty set of elements called vertices and eg is a set possibly empty of unordered pairs u,v of vertices u,v.
A total edgemagic graph is called a super edgemagic if fvg 1,2. We also study directed graphs or digraphs d v,e, where the edges have a direction, that is, the. A characterization of regular magic graphs in terms of cycles. We show that there is at least one 3regular xormagic graph on 2 n vertices for every n. In this paper, the necessary and sufficient conditions for the existence of degreemagic labelings of graphs obtained by taking the join and. The problem of identifying which kinds of super edgemagic graphs are weakmagic graphs is addressed in this paper. Totally magic graphs a complete search on small graphs one of the. Some of their properties are also discussed with suitable examples. Magic and antimagic labeling of graphs researchgate. Also a graph g which admits a super edge magic graceful labeling is called a super edge. In other words any edge econnecting vertex uto vertex vcan be uniquely writen as e fu. A circuit starting and ending at vertex a is shown below.
List of theorems mat 416, introduction to graph theory 1. 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. Magic valuations of finite graphs canadian mathematical. E wherev isasetofvertices andeisamultiset of unordered pairs of vertices. Connected a graph is connected if there is a path from any vertex. This concise, selfcontained exposition is unique in its focus on the theory of magic graphs. In this paper we determine the distance magic index of trees and complete bipartite graphs. 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. The pdf file you selected should load here if your web browser has a pdf reader plugin installed for example, a recent version of adobe acrobat reader if you would like more information about how to print, save, and work with pdfs, highwire press provides a helpful frequently asked questions about pdfs. Introduction in 20th century, remarkable development had happened. Ngurah and rinovia simanjuntak, on the super edgemagic deficiency of join product and chain graphs, electron. Degreemagic labelings on the join and composition of. E g or f uv graphs, or parallel algorithms will not be treated.
For most of the graph theory terminology and notation used, we follow chartrand and lesniak 1 throughout this paper. 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. Graph theory 3 a graph is a diagram of points and lines connected to the points. Antimagic orientations of even regular graphs li 2019. Magic labelings magic squares are among the more popular mathematical. The basis of graph theory is in combinatorics, and the role of graphics is.
The concept of graphs in graph theory stands up on. In recent years, graph theorists have extended this basic idea to graphs. We write vg for the set of vertices and eg for the set of edges of a graph g. Graph is a mathematical representation of a network and it describes the relationship between lines and points. Let g be an avertex consecutive magic graph of n vertices and e n edges. Degree magic graphs extend supermagic regular graphs.
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 or two deeper results, again with proofs given in full detail. This chapter summarizes the basic concepts of graph theory and introduces the notation used in this work. Jun 30, 2016 cs6702 graph theory and applications 1 cs6702 graph theory and applications unit i introduction 1. Mathematics graph theory basics set 1 geeksforgeeks. Looking for avertex consecutive magic graphs with e n and minimum degree one, we show the following result. Cs6702 graph theory and applications notes pdf book. This monograph is a complete account of magic and antimagic graph labelings. The question studied in this paper is for which bipartite graphs it is possible to add a finite number of isolated vertices so that the resulting graph is consecutively super edgemagic. 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. A magic square is an arrangement of numbers into a square such that the sum of each row, column and. For most of the graph theory terminology and notation used, we follow chartrand.
On the super edgemagic deficiency of join product and chain. Connected a graph is connected if there is a path from any vertex to any other vertex. Determine wether these graphs are semimigic or magic the. The question about the existence of such valuations arises from the investigation of another kind of valuations which are introduced in 1 and are related to cyclic decompositions of complete graphs into isomorphic subgraphs. List of theorems mat 416, introduction to graph theory. An edge magic labeling f of a graph with p vertices and q edges is a bijection f. Another important open problem to look into is, whether there exists an edge magic labeling for a general ncm graph for m3 and 0 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. Math 215 project number 1 graph theory and the game.
Graphtheoretic applications and models usually involve connections to the real. Magic and antimagic labelings are among the oldest labeling schemes in graph theory. Fuzzy graph, fuzzy magic graph, fuzzy matrix, adjacency matrix, incidence matrix. In these algorithms, data structure issues have a large role, too see e. The problem of identifying which kinds of super edge magic graphs are weak magic graphs is addressed in this paper. In this paper, the necessary and sufficient conditions for the existence of degree magic labelings of graphs obtained by taking the join and composition of complete tripartite graphs are found. Math 215 project number 1 graph theory and the game of. Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one. Tkac, on the degrees of a super vertex magic graph, discrete math. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called. General definitions of cycles, wheels, fans, friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic. If both summands on the righthand side are even then the inequality is strict. In general, all the graphs are not prime, it is very interesting to investigate graph families which admit prime labelling. In the course of the problems we shall also work on writing proofs that use mathematical.
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. The consecutively super edgemagic deficiency of graphs. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond. 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 graph consists of some points and lines between them. The basis of graph theory is in combinatorics, and the role of graphics is only in visualizing things.
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. Graph theory 64 2010 219232 initiated the study of antimagic labelings of digraphs, and conjectured that every connected graph admits an antimagic orientation, where an orientation. It has at least one line joining a set of two vertices with no vertex connecting itself. A total edge magic graph is called a super edge magic if fvg 1,2.
Also a graph g which admits a super edge magic graceful labeling is called a super edge magic graceful graph. In this paper different types of matrices in some fuzzy magic graphs such as path, cycle are introduced. Magic graphs books pics download new books and magazines. Mi,j 0 if there is no edge from i to j, if there is an edge mi,j 1.
On the super edgemagic deficiency of join product and. For all standard notation and terminology in graph theory we follow 4. The purpose of this paper is to investigate for graphs the existence of certain valuations which have some magic property. Prove that a bipartite graph with odd number of vertices is non magic. S, where the minimum is taken over all sets s for which the graph g admits an smagic labeling. It comprehensively covers super magic graphs, total labelings, vertex magic total labelings, edge magic total labelings. In this paper, the edgemagic labelings of ncm and some other graphs are discussed. The pdf file you selected should load here if your web browser has a pdf reader plugin installed for example, a recent version of adobe acrobat reader if you would like more information about how to. Let g be an avertex consecutive magic graph of n vertices and e n. Degreemagic graphs extend supermagic regular graphs. Kotzig and rosa called such a labeling, and the graph possessing it, magic.