Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one fig1. On the super edgemagic deficiency of join product and chain. 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 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 total edgemagic graph is called a super edgemagic if fvg 1,2. Magic and antimagic graphs attributes, observations and. It has at least one line joining a set of two vertices with no vertex connecting itself.
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. 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. Cycle is a graph where there is an edge between the adjacent vertices only and the vertex is adjacent to last one. In other words any edge econnecting vertex uto vertex vcan be uniquely writen as e fu. A graph is a finite set of vertices and edges where every edge connects two vertices. Degreemagic labelings on the join and composition of. In this paper, the edgemagic labelings of ncm and some other graphs are discussed. S, where the minimum is taken over all sets s for which the graph g admits an smagic labeling. The basis of graph theory is in combinatorics, and the role of graphics is. Graphtheoretic applications and models usually involve connections to the real. We also study directed graphs or digraphs d v,e, where the edges have a direction, that is, the edges are ordered.
Math 215 project number 1 graph theory and the game. In the course of the problems we shall also work on writing proofs that use mathematical. 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. Graph theory 121 circuit a circuit is a path that begins and ends at the same vertex. An edge magic graceful labeling of a graph g is super edge magic graceful if the set of vertex labels is 1, 2, p. The concept of graphs in graph theory stands up on. The purpose of this paper is to investigate for graphs the existence of certain valuations which have some magic property. In this paper we determine the distance magic index of trees and complete bipartite graphs. The problem of identifying which kinds of super edgemagic graphs are weakmagic graphs is addressed in this paper. 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. E g or f uv graphs, or parallel algorithms will not be treated.
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. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the. Magic graphs books pics download new books and magazines. 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. List of theorems mat 416, introduction to graph theory 1. 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 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.
Some of their properties are also discussed with suitable examples. 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. Also, jgj jvgjdenotes the number of verticesandeg jegjdenotesthenumberofedges. 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. On the super edgemagic deficiency of join product and.
The consecutively super edgemagic deficiency of graphs. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called. Magic and antimagic labelings are among the oldest labeling schemes in graph theory. In these algorithms, data structure issues have a large role, too see e. 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. Degreemagic graphs extend supermagic regular graphs. This monograph is a complete account of magic and antimagic graph labelings. Jun 30, 2016 cs6702 graph theory and applications 1 cs6702 graph theory and applications unit i introduction 1. The basis of graph theory is in combinatorics, and the role of graphics is only in visualizing things.
This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond. Degree magic graphs extend supermagic regular graphs. This chapter summarizes the basic concepts of graph theory and introduces the notation used in this work. Mathematics graph theory basics set 1 geeksforgeeks. A circuit starting and ending at vertex a is shown below. It comprehensively covers super magic graphs, total labelings, vertex magic total labelings, edge magic total labelings. A graph consists of some points and lines between them. We also study directed graphs or digraphs d v,e, where the edges have a direction, that is, 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 print, save, and work with pdfs, highwire press provides a helpful frequently asked questions about pdfs. Prove that a bipartite graph with odd number of vertices is non magic. Differential geometry in graphs harvard university. 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 of. A graph is a diagram of points and lines connected to the points. Graph theory 3 a graph is a diagram of points and lines connected to the points. List of theorems mat 416, introduction to graph theory. A graph is a data structure that is defined by two components. 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.
The problem of identifying which kinds of super edge magic graphs are weak magic graphs is addressed in this paper. Mi,j 0 if there is no edge from i to j, if there is an edge mi,j 1. An element of the edge set is a twoelement subset of the vertex set. An edge e or ordered pair is a connection between two nodes u,v.
Magic and antimagic labeling of graphs researchgate. General definitions of cycles, wheels, fans, friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic. We write vg for the set of vertices and eg for the set of edges of a graph g. In this paper different types of matrices in some fuzzy magic graphs such as path, cycle are introduced. For all standard notation and terminology in graph theory we follow 4. An edge magic labeling f of a graph with p vertices and q edges is a bijection f. 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 valuations of finite graphs canadian mathematical. A magic square is an arrangement of numbers into a square such that the sum of each row, column and. A total edge magic graph is called a super edge magic if fvg 1,2. If both summands on the righthand side are even then the inequality is strict. Tkac, on the degrees of a super vertex magic graph, discrete math. In general, all the graphs are not prime, it is very interesting to investigate graph families which admit prime labelling.
Connected a graph is connected if there is a path from any vertex. 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. Looking for avertex consecutive magic graphs with e n and minimum degree one, we show the following result. Fuzzy graph, fuzzy magic graph, fuzzy matrix, adjacency matrix, incidence matrix. Connected a graph is connected if there is a path from any vertex to any other vertex. Cs6702 graph theory and applications notes pdf book. 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. A characterization of regular magic graphs in terms of cycles. The question about the existence of such valuations arises from. 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.
Department of mathematics, university of manitoba, winnipeg, manitoba. Antimagic orientations of even regular graphs li 2019. Let g be an avertex consecutive magic graph of n vertices and e n edges. Totally magic graphs a complete search on small graphs one of the.
The length of the lines and position of the points do not matter. E wherev isasetofvertices andeisamultiset of unordered pairs of vertices. Kotzig and rosa called such a labeling, and the graph possessing it, magic. Let g be an avertex consecutive magic graph of n vertices and e n. In recent years, graph theorists have extended this basic idea to graphs. This concise, selfcontained exposition is unique in its focus on the theory of magic graphs.
In this paper, the necessary and sufficient conditions for the existence of degreemagic labelings of graphs obtained by taking the join and. The game is called sprouts and it is an invention of john horton conway. A typical directed graph this graph can be represented by a matrix m, called the adjacency matrix, as shown below. Determine wether these graphs are semimigic or magic the. Jun 12, 2018 motivated by the conjecture of hartsfield and ringel from 1990 on antimagic labelings of graphs, hefetz, mutze, and schwartz on antimagic directed graphs, j. 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 labelings magic squares are among the more popular mathematical. Magic and antimagic labeling of graphs kiki ariyanti sugeng this thesis is submitted in total ful. 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 is a mathematical representation of a network and it describes the relationship between lines and points. Also a graph g which admits a super edge magic graceful labeling is called a super edge.
1134 1434 606 1049 490 1376 510 1592 1441 689 944 1422 613 330 782 560 1357 286 902 96 36 139 240 422 1493 248 1181 1436 149 1129 1039 139 808 748 1447 1592 1598 1155 1321 256 1213 744 179 513 856 89 1477 131 70