A metaheuristic approach to the graceful labeling problem. This labeling was originally introduced in 1967 by rosa. In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with some subset of the integers between 0 and m inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints, such that this magnitude lies between 1 and m inclusive. Diestel is excellent and has a free version available online. To be more precise, if we assume g v, e to be an undirected graph without loops or double connections between vertices, a graceful.
Applications of mathematical programming in graceful labeling of graphs. The odd graceful labeling is one of the most widely used labeling methods of graphs 18. Aimed toward upper undergraduate and graduate students in mathematics, this book examines the foremost forms of graph labelings including magic, harmonious, and graceful labelings. Graceful labeling graceful graph ringelkotzig conjecture. A graph which admits a fuzzy graceful labeling is called a fuzzy graceful graph. Magic and antimagic graphs attributes, observations and. A related problem called harmonious labeling was shown to be npcomplete. First, i like this book and gave it 5 stars but it is not the best book on graph theory, though it is a great intro. Graceful, harmonious and magic type labelings relations. The field of graph theory plays an important role in. Let be a graph obtained by replacing each vertices. Theory and applications labeled graphs are becoming an increasingly useful family of mathematical models for a broad range of applications. By omitting all edges with duplicate numbers we can get a graceful graph that golomb calls a graceful approximation of a complete graph.
Identify the edges of with suitable edges of, where q eg 3. In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with some subset of the integers between 0 and m inclusive, such that no. Introduction a graph g of size q is oddgraceful, if there is an injection. Recreational problems of this type have been discussed before in my earlier book collections. Concluding remarks we introduced here a new graph is called cycle of graphs.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. Several authors worked on graceful labeling, odd graceful labeling, even graceful labeling, super graceful labeling and skolem graceful labeling. While the labeling of graphs is perceived to be a primarily theoretical subject in the field of graph theory and discrete mathematics, it serves as models in a wide range of applications as listed below. A graph g with q edges is said to be odd graceful if there is an injection f. The 7page book graph of this type provides an example of a graph with no harmonious labeling. Applications of graph theory in protein structure identification. Where this book shines is the presenation of a wide variety of. A new labeling with a connection to the four color theorem is described to aid mathematicians to initiate new methods and techniques to study classical coloring problems from a new perspective. 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.
Introduction to graph theory 2nd edition by west solution manual 1 chapters updated apr 03, 2019 06. Applications of graph labeling in communication networks. An edgegraceful labelling on a simple graph without loops or multiple edges on p vertices and q edges is a labelling of the edges by distinct integers in 1, q such that the labelling on the vertices induced by labelling a vertex with the sum of the incident edges taken modulo p assigns all values from 0 to p. Theory and applications graph labelings, where the vertices and edges are assigned, real values subject to certain conditions, have often been motivated by their utility to various applied fields and their intrinsic mathematical interest logico mathematical. Odd graceful labeling of acyclic graphs science publishing. An overview of basic graph theory concepts and notation is provided along with the origins of graph labeling. A graph is called graceful if it has at least one such labeling. The purpose of this book is to provide some results in a class of. Abstract a method to obtain all possible graceful spanning trees in a complete graph is proposed. Graph theory and computing focuses on the processes, methodologies, problems, and approaches involved in graph theory and computer science.
Finally, we introduce a new conjecture the revised friendship graph fkc n is odd graceful where k is any positive integer and n 0 mod 4. A graph g is called graceful if it has a graceful labeling. The 7page book graph of this type provides an example of a graph with no harmonious labeling a second type, which might be called a triangular book, is the complete. Likewise, an edge labelling is a function of to a set of labels. It is not the easiest book around, but it runs deep and has a nice unifying theme of studying how. The name graceful labeling was coined later by golomb.
What are some good books for selfstudying graph theory. Gracefully labeled graphs serve as models in a wide range of applications including coding theory and communication network addressing. Introductory graph theory dover books on mathematics. Improve approximate factors of relaxed graceful labeling bussel02. This book depicts graph labelings that have led to thoughtprovoking problems and conjectures. Researchers and graduate students interested in graph labelings will find the concepts and problems featured in this book valuable for finding new areas. Gracefully labeled graphs serve as models in a wide range of applications including coding. In graph theory, graceful labelings and graceful graphs have been studied for over forty years, since their introduction by rosa, 1966. A valuation on a simple graph g is an assignment of labels to the vertices of g which induces an assignment of labels to the edges of g. For example, by dropping one edge the line between points 1 and 4 from a complete graph for five points see figure 93 the graph can be gracefully numbered.
The injective mapping is called graceful if the weight of edge are all different for every edge xy. The labeling pattern is demonstrated by means of illustrations, which provide better understanding of derived results. Fuzzy vertex graceful labeling on wheel and fan graphs. Graph theory is an area in discrete mathematics which studies configurations called graphs involving a set of vertices interconnected by edges. That is, it is a cartesian product of a star and a single edge.
Some labeling with variations in graceful theme are also. Part of the lecture notes in computer science book series lncs, volume 6552. Z, in other words it is a labeling of all edges by integers. An algorithm to generate all the labeled spanning trees in a complete graph is developed and modified to generate all graceful spanning trees. Most of these topics have been discussed in text books.
On sequential labelings of graphs grace 1983 journal of. A bit of history the concept of graceful labeling was initially used to attack the problem of the decomposition of graphs. A new graceful labeling for pendant graphs springerlink. A graph g with q edges is said to be oddgraceful if there is an injection f.
Edge even graceful labelingwas first defined byelsonbaty and daoud in 2017. Research directions, contains ten articles, mainly survey type, on some current research areas in graph theory, namely, graceful labeling, l2,1labelling, complexity of graph labeling problems, dominations, interval graphs, matrices and graphs. As we mention there the ringel conjecture and many efforts to settle it provided the reason for various graph labeling problems. Some topics in graph theory the purpose of this book is to provide some results in a class of problems categorized as graph labeling. The crossreferences in the text and in the margins are active links. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading. This is a labeling for simple graphs in which no two distinct edges connect the same.
There is a part of graph theory which actually deals with graphical drawing and presentation of graphs, brie. A graceful labeling in a graph with p vertices and q edges is assigning the numbers to the vertices 0,1,2,q. For many, this interplay is what makes graph theory so interesting. Second, in this model, each score can be calculated fast, which makes the computation easy to accomplish. Introduction to graceful graphs 2 acknowledgment i am deeply indebted to my late supervisor prof. A graph in this context is made up of vertices also called nodes or points which are connected by edges also called links or lines. A labeling of a graph is an assignment of values to the vertices and edges of a graph. In addition, the book covers an assortment of variations on the labeling theme, all in one selfcontained monograph.
An edge even graceful labeling of a simple graph g with p vertices and q edges is a bijection f from the edges of the graph to the set 2, 4, 2 q such that, when each vertex is assigned the sum of all edges incident to it mod 2 r where r max p, q, the resulting vertex labels are distinct. The book first elaborates on alternating chain methods, average height of planted plane trees, and numbering of a graph. One of the least explored areas of modern mathematics is a class of problems that combine graph theory and arithmetic. If fv nf p be the fibonacci number other then f q 1 and f q 2 then jfv n fv 1j jf p f qjcan not be fibonacci number for jp qj2 case 2. May 16, 2018 the field of graph theory plays an important role in. The edge even graceful labeling of some triangular graphs are shown in figure 7.
The second chapter is devoted to introduce the main labelings discussed. If the resulting graph edge numbers run from 1 to inclusive, the labeling is a graceful labeling and the graph is. A graceful labeling or graceful numbering is a special graph labeling of a graph on edges in which the nodes are labeled with a subset of distinct nonnegative integers from 0 to and the graph edges are labeled with the absolute differences between node values. First, it transfers a protein structure identification problem to a graph theory one, uses the algorithm of graph theory clique finding to solve it and makes the original problem easier to handle. Grid paper notebook, quad ruled, 100 sheets large, 8. Graceful, harmonious and magic type labelings relations and. It is a graph consisting of triangles sharing a common edge. A graceful labeling of a graph g with q edges is an injective assignment of labels from 0, 1. Doublewheel graphs are graceful cornell university. Graceful labeling is one of the interesting topics in graph theory.
Assuming only basic familiarity with graphs, this book, complete with carefully written proofs of most results, is an ideal introduction to graph labeling for students learning the subject. Square graceful labeling of some graphs open access journals. Some of the major themes in graph theory are shown in figure 3. An example usage of graph theory in other scientific. We discussed here graceful labeling for cycle of graphs. In this paper we introduced fuzzy vertex gracefulness and discussed to wheel graphs and fan graphs. Introduction a graph g of size q is odd graceful, if there is an injection. Keywords graph theory, odd graceful labeling, friendship graphs. The notes form the base text for the course mat62756 graph theory. In graph theory, an edgegraceful graph labeling is a type of graph labeling. Golombs graceful graphs mathematical amusements magical. Find the top 100 most popular items in amazon books best sellers. Let g v, e be a finite, simple and undirected graph. They contain an introduction to basic concepts and results in graph theory, with a special emphasis put on the networktheoretic circuitcut dualism.
Eg is assigned the label fx fy, all of the edge labels are distinct. A graph with such a labeling is an edge labeled graph. Jun 23, 2009 complexity of graceful labeling is open. Odd graceful labeling of the revised friendship graphs. In graph theory, a graceful labeling of a graph g v, e with n vertices and m edges is a labeling of its vertices with distinct integers between 0 and m inclusive, such that each edge is uniquely identified by the absolute difference between its endpoints.
A labeling graph g which can be gracefully numbered is said to be graceful. On sequential labelings of graphs grace 1983 journal. The existence of a graceful labeling of a given graph g with n edges is a sufficient condition for the existence of a cyclic decomposition of a complete graph of. Further results on super graceful labeling of graphs. 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. For k 1, the function f is called a super graceful labeling and a graph is super graceful if it admits a super graceful labeling. In graph theory, a graceful labeling of a graph g v, e with n vertices and m edges is a labeling of its vertices with distinct integers between 0 and m.
Fibonacci and super fibonacci graceful labeling of some graphs 107 if fv 2f q 1 then fv n,f q 2 otherwise fv 1v n fvv 2f q 1. He introduced me to the world of graph theory and was always patient, encouraging and resourceful. On graceful labeling of some graphs with pendant edges. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph. In this paper, we study the super gracefulness of complete graph, the disjoint union of certain star graphs, the complete tripartite graphs k 1, 1, n, and certain families of trees. Rosa67 alex rosa, on certain valuations of the vertices of a graph. Haggkvist conjectured that if g is a 2m regular graph and t is a tree with m edges then eg decomposes into n copies of t.
Chapter 5 fibonacci graceful labeling of some graphs. Problems and conjectures in graceful labelings, harmonious labelings, prime labelings, additive labelings, and zonal labelings are introduced with fundamentals, examples, and illustrations. The notation and terminology used in this paper are taken from gallian 9. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at h3 level in the new. Let g be an undirected graph without loops or double connections between vertices. An example usage of graph theory in other scientific fields. Symmetry free fulltext edge even graceful labeling of. A second type, which might be called a triangular book, is the complete tripartite graph k 1,1,p.
Rosa, a on certain valuations of the vertices of a graph, theory of graphs. Qualitative labelings of graph elements have inspired research in diverse fields of human enquiry such as conflict resolution in social psychology. For detail survey of graph labeling one can refer gallian gallian 20. Pdf edge even graceful labelling of some book graphs. Mehendale sir parashurambhau college, pune411030, india. If is a fixed tree with edges, then complete graph on vertices decomposes into copies of. Determining whether a graph has a harmonious labeling was shown to be npcomplete by auparajita, dulawat, and rathore in 2001 see 833. The field of graph theory plays an important role in various areas of pure and applied sciences. There are several types of graph labeling and a detailed survey is found in 4. Pdf graceful labeling of some graphs and their subgraphs. Fibonacci and super fibonacci graceful labeling of some graphs 103 5. The graceful labeling was introduced by rosa rosa 1967, p. A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where. One kind, which may be called a quadrilateral book, consists of p quadrilaterals sharing a common edge known as the spine or base of the book.
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