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. A characterization of regular magic graphs in terms of cycles. Raziya begam tree with three vertices and s2 a star on three vertices then t3 s2 is formed as follows. 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. General definitions of cycles, wheels, fans, friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic. Magic squares can trace their origin back to ancient china somewhere around the 7th century bce 4. In this paper different types of matrices in some fuzzy magic graphs such as path, cycle are introduced. In other words any edge econnecting vertex uto vertex vcan be uniquely writen as e fu. Also a graph g which admits a super edge magic graceful labeling is called a super edge magic graceful graph. Introduction in 20th century, remarkable development had happened. Kotzig and rosa called such a labeling, and the graph possessing it, magic.
Graph is a mathematical representation of a network and it describes the relationship between lines and points. Magic valuations of finite graphs canadian mathematical. Fuzzy graph, fuzzy magic graph, fuzzy matrix, adjacency matrix, incidence matrix. In recent years, graph theorists have extended this basic idea to graphs. Prove that a bipartite graph with odd number of vertices is non magic.
We show that there is at least one 3regular xormagic graph on 2 n vertices for every n. An element of the edge set is a twoelement subset of the vertex set. A graph consists of some points and lines between them. This chapter summarizes the basic concepts of graph theory and introduces the notation used in this work. For graph theory notations and terminology not described in this paper, the readers are referred to 1. Department of mathematics, university of manitoba, winnipeg, manitoba. Let g be an avertex consecutive magic graph of n vertices and e n. 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. 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. Also a graph g which admits a super edge magic graceful labeling is called a super edge. Totally magic graphs a complete search on small graphs one of the. Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one fig1. A total edgemagic graph is called a super edgemagic if fvg 1,2. This concise, selfcontained exposition is unique in its focus on the theory of magic graphs.
A total edge magic graph is called a super edge magic if fvg 1,2. List of theorems mat 416, introduction to graph theory. Connected a graph is connected if there is a path from any vertex to any other vertex. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond. In this paper, the necessary and sufficient conditions for the existence of degreemagic labelings of graphs obtained by taking the join and. The length of the lines and position of the points do not matter. Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one. Graph theory 121 circuit a circuit is a path that begins and ends at the same vertex. Graphtheoretic applications and models usually involve connections to the real. General definitions of cycles, wheels, fans, friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic labeling are as follows. In this paper we determine the distance magic index of trees and complete bipartite graphs.
The intriguing question is to decide which graphs are edge magic or vertex magic, or both. Graph theory 3 a graph is a diagram of points and lines connected to the points. An edge e or ordered pair is a connection between two nodes u,v. This monograph is a complete account of magic and antimagic graph labelings. Connected a graph is connected if there is a path from any vertex. Magic and antimagic labeling of graphs researchgate. A graph is a data structure that is defined by two components. 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. On the super edgemagic deficiency of join product and chain. Degree magic graphs extend supermagic regular graphs. Magic and antimagic labelings are among the oldest labeling schemes in graph theory. A magic square is an arrangement of numbers into a square such that the sum of each row, column and. A graph is a finite set of vertices and edges where every edge connects two vertices.
E g or f uv graphs, or parallel algorithms will not be treated. We write vg for the set of vertices and eg for the set of edges of a graph g. The consecutively super edgemagic deficiency of graphs. Also, jgj jvgjdenotes the number of verticesandeg jegjdenotesthenumberofedges. The problem of identifying which kinds of super edge magic graphs are weak magic graphs is addressed in this paper. Magic and antimagic labeling of graphs kiki ariyanti sugeng this thesis is submitted in total ful. It may seem strange to term a graph as having an \antimagic labeling, but the term comes from its connection to magic labelings and magic squares. For most of the graph theory terminology and notation used, we follow chartrand.
The game is called sprouts and it is an invention of john horton conway. 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 graphs books pics download new books and magazines. Some of their properties are also discussed with suitable examples. Magic labelings magic squares are among the more popular mathematical. Let g be an avertex consecutive magic graph of n vertices and e n edges. The question about the existence of such valuations arises from. Mi,j 0 if there is no edge from i to j, if there is an edge mi,j 1. The concept of graphs in graph theory stands up on. An edge magic labeling f of a graph with p vertices and q edges is a bijection f. 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 basis of graph theory is in combinatorics, and the role of graphics is. 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. It comprehensively covers super magic graphs, total labelings, vertex magic total labelings, edge magic total labelings.
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. Jun 30, 2016 cs6702 graph theory and applications 1 cs6702 graph theory and applications unit i introduction 1. 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. Math 215 project number 1 graph theory and the game of. A typical directed graph this graph can be represented by a matrix m, called the adjacency matrix, as shown below. Looking for avertex consecutive magic graphs with e n and minimum degree one, we show the following result. 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. Ngurah and rinovia simanjuntak, on the super edgemagic deficiency of join product and chain graphs, electron. For most of the graph theory terminology and notation used, we follow chartrand and lesniak 1 throughout 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. 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. Cs6702 graph theory and applications notes pdf book. An edge magic graceful labeling of a graph g is super edge magic graceful if the set of vertex labels is 1, 2, p. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the.
E wherev isasetofvertices andeisamultiset of unordered pairs of vertices. Murty, graph theory with applications, macmillan, lon. The purpose of this paper is to investigate for graphs the existence of certain valuations which have some magic property. 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. 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.
We also study directed graphs or digraphs d v,e, where the edges have a direction, that is, the. Degreemagic labelings on the join and composition of. List of theorems mat 416, introduction to graph theory 1. Differential geometry in graphs harvard university. Math 215 project number 1 graph theory and the game. Antimagic orientations of even regular graphs li 2019. 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. We also study directed graphs or digraphs d v,e, where the edges have a direction, that is, the edges are ordered. In general, all the graphs are not prime, it is very interesting to investigate graph families which admit prime labelling. Tkac, on the degrees of a super vertex magic graph, discrete math. For all standard notation and terminology in graph theory we follow 4.
S, where the minimum is taken over all sets s for which the graph g admits an smagic 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 or two deeper results, again with proofs given in full detail. A circuit starting and ending at vertex a is shown below. Determine wether these graphs are semimigic or magic the. 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. Mathematics graph theory basics set 1 geeksforgeeks. In the course of the problems we shall also work on writing proofs that use mathematical.
It has at least one line joining a set of two vertices with no vertex connecting itself. On the super edgemagic deficiency of join product and. If both summands on the righthand side are even then the inequality is strict. 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. Magic and antimagic graphs attributes, observations and. In these algorithms, data structure issues have a large role, too see e. Degreemagic graphs extend supermagic regular graphs. The problem of identifying which kinds of super edgemagic graphs are weakmagic graphs is addressed in this paper.
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