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. Pdf graceful labeling of some graphs and their subgraphs. A graph which admits a graceful labeling is called a. Each vertex and each edge of is rotated times from the original position. On sequential labelings of graphs grace 1983 journal of. The use of graphs in wiring diagrams is a straightforward representation of the physical elements of an electrical circuit. 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. The graceful labeling was introduced by rosa rosa 1967, p. In addition, the book covers an assortment of variations on the labeling theme, all in one selfcontained monograph.
It is not the easiest book around, but it runs deep and has a nice unifying theme of studying how. Gracefully labeled graphs serve as models in a wide range of applications including coding. A graceful labeling of a graph g with q edges is an injective assignment of labels from 0, 1. Introduction a graph g of size q is oddgraceful, if there is an injection. Some of the major themes in graph theory are shown in figure 3. The field of graph theory plays vital role in various fields. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph. If is a fixed tree with edges, then complete graph on vertices decomposes into copies of. Graph theory has existed for many years not only as an area of mathematical study but also as an intuitive and illustrative tool. We denote here a star graph as s where r number of pendant vertices are connected to one vertex.
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. Vertex graceful labeling of some classes of graphs scielo. Golomb called such labelings graceful and this term is followed presently. Gracefully labeled graphs serve as models in a wide range of applications including coding theory and communication network addressing. The book is clear, precise, with many clever exercises and many excellent figures. As we mention there the ringel conjecture and many efforts to settle it provided the reason for various graph labeling problems. Graceful labeling i for a connected graph g with q edges, a vertex labeling f. Graceful labeling for corona and flower graph aip publishing. 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.
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. A graph is called graceful if it has at least one such labeling. A graph g is called graceful if it has a graceful labeling. Pdf graceful labeling for some supercaterpillar graphs. Applications of graph labeling in communication networks. Labeling, graceful labeling, cycle, complete bipartite graph, cycle of graphs. Golomb 7 called such labelings graceful and this term is followed presently. Pdf edge even graceful labelling of some book graphs. 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. 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. Graceful, harmonious and magic type labelings relations and.
There are several types of graph labeling and a detailed survey is found in 4. I such a labeling is called graceful if the edges are labeled 1. Graceful labeling is one of the interesting topics in graph theory. Several authors worked on graceful labeling, odd graceful labeling, even graceful labeling, super graceful labeling and skolem graceful labeling. Keywords graph theory, odd graceful labeling, friendship graphs. Magic and antimagic graphs attributes, observations and. The notation and terminology used in this paper are taken from gallian 9.
The graceful labeling of the graph then corresponds to the. V 0, 1, e is called graceful if the weight of edge wuv fu. This concisely written textbook is intended for an introductory course in graph theory for undergraduate mathematics majors or advanced undergraduate and graduate students from the many fields that benefit from graphtheoretic applications. The book can be used as a reliable text for an introductory course, as a graduate text, and for selfstudy. The labeling pattern is demonstrated by means of illustrations, which provide better understanding of derived results. The notes form the base text for the course mat62756 graph theory. Diestel is excellent and has a free version available online. Some labeling with variations in graceful theme are also. Determining whether a graph has a harmonious labeling was shown to be npcomplete by auparajita, dulawat, and rathore in 2001 see 833.
A new graceful labeling for pendant graphs springerlink. Let be a graph obtained by replacing each vertices. A metaheuristic approach to the graceful labeling problem. Fibonacci and super fibonacci graceful labeling of some graphs 103 5. 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. Jun 24, 2019 there are different types of labeling such as graceful labeling, magic labeling, edgegraceful labeling, prime labeling, radio labeling, harmonious labeling etc.
The dots are called nodes or vertices and the lines are called edges. 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. A bit of history the concept of graceful labeling was initially used to attack the problem of the decomposition of graphs. The injective mapping is called graceful if the weight of edge are all different for every edge xy. Let be a graph obtained by replacing each vertices of except the apex vertex by the graph let is the. Most of these topics have been discussed in text books. Introductory chapters present the main ideas and topics in graph theorywalks, paths and. In this work we introduce a new graph which is called cycle of graphs and it is denoted by cg1,g2.
Instead, it was determined that approximately of the edges of kn. 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. Let g be an undirected graph without loops or double connections between vertices. C n denotes a cycle on n vertices and k m,n denotes. Some topics in graph theory the purpose of this book is to provide some results in a class of problems categorized as graph labeling. Further results on super graceful labeling of graphs. As a research area, graph theory is still relatively young, but it is maturing rapidly with many deep results having been discovered over the last couple of decades. Given a graph consisting of vertices and edges, a vertex labeling of is an assignment of labels to the vertices of that produces for each edge a label depending.
The field of graph theory plays an important role in. Free graph theory books download ebooks online textbooks. Doublewheel graphs are graceful cornell university. Concluding remarks we introduced here a new graph is called cycle of graphs. Graph theory is an area in discrete mathematics which studies configurations called graphs involving a set of vertices interconnected by edges. Applications of graph theory in protein structure identification. On graceful labeling of some graphs with pendant edges. They contain an introduction to basic concepts and results in graph theory, with a special emphasis put on the networktheoretic circuitcut dualism. Identify the edges of with suitable edges of, where q eg 3. The odd graceful labeling is one of the most widely used labeling methods of graphs 18. Find the top 100 most popular items in amazon books best sellers. Graceful labeling for open star of graphs by invention. Z, in other words it is a labeling of all edges by integers. The edge even graceful labeling of some triangular graphs are shown in figure 7.
One of the important areas in graph theory is graph labeling used in many applications like coding theory, xray crystallography, radar, astronomy, circuit design, communication network addressing, data base management. The proofs of the theorems are a point of force of the book. Also we have defined a flower graph which does not admit. Odd graceful labeling of the revised friendship graphs.
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. It cover the average material about graph theory plus a lot of algorithms. A graph g with q edges is said to be oddgraceful if there is an injection f. There are different types of labeling such as graceful labeling, magic labeling, edgegraceful labeling, prime labeling, radio labeling, harmonious labeling etc.
Chapter 5 fibonacci graceful labeling of some graphs. A graph with such a labeling is an edge labeled graph. 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. This book depicts graph labelings that have led to thoughtprovoking problems and conjectures. The second chapter is devoted to introduce the main labelings discussed. 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. Over the past three decades in excess of 800 papers have spawned a bewildering array of graph labeling methods. The purpose of this book is to provide some results in a class of.
The book edited by acharia, arumugam and rosa 1 includes a variety of labeling. Odd graceful labeling of acyclic graphs science publishing. It has every chance of becoming the standard textbook for graph theory. We discussed here graceful labeling for cycle of graphs. This outstanding book cannot be substituted with any other book on the present textbook market. Introduction a graph g of size q is odd graceful, if there is an injection. Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to practical problems. A graph which admits odd graceful labeling is called an odd graceful graph. The book edited by acharia, arumugam and rosa includes a variety of labeling. Inclusionexclusion, generating functions, systems of distinct representatives, graph theory, euler circuits and walks, hamilton cycles and paths, bipartite graph, optimal spanning trees, graph coloring, polyaredfield counting. Pdf graceful labeling of some graphs iir publications. Square graceful labeling of some graphs open access journals.
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