I used this book to teach a course this semester, the students liked it and it is a very good book indeed. The name graceful labeling was coined later by golomb. It is a graph consisting of triangles sharing a common edge. Some labeling with variations in graceful theme are also. In section 5, some results using computer software in the field of graph labelings. 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 labeling pattern is demonstrated by means of illustrations, which provide better understanding of derived results. Diestel is excellent and has a free version available online. 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.
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. A graph g with q edges is said to be odd graceful if there is an injection f. Graceful labeling is one of the interesting topics in graph theory. The famous conjecture in graceful labeling is all trees are graceful. Let g v, e be a finite, simple and undirected graph. Graph labelings give us useful models for a wide range of applications such as coding theory, xray, astronomy, radar, and communication. Vertex graceful labeling of some classes of graphs scielo. This book depicts graph labelings that have led to thoughtprovoking problems and conjectures. A graceful labeling in a graph with p vertices and q edges is assigning the numbers to the vertices 0,1,2,q.
An example usage of graph theory in other scientific fields. Acharya 22 proved that every graph can be embedded as an induced subgraph of a graceful graph and a connected graph can be embedded as an induced subgraph of a graceful connected graph. A new graceful labeling for pendant graphs springerlink. Several authors worked on graceful labeling, odd graceful labeling, even graceful labeling, super graceful labeling and skolem graceful labeling. The 7page book graph of this type provides an example of a graph with no harmonious labeling. Graceful labeling for open star of graphs by invention. The book edited by acharia, arumugam and rosa includes a variety of. Solairaju and chithra introduced a new type of labeling of a graph g with p vertices and q edges called an edge odd graceful labeling if there is a bijection f from the edges of the graph to the set 1, 3, 2 q. In addition, we use a graceful labeling to represent a 0, 1. In this paper, we obtained an edge even graceful labeling for some pathrelated graphs like y tree, the double star bn,m, the graph.
Edge odd graceful labeling of some path and cycle related. Grid paper notebook, quad ruled, 100 sheets large, 8. Introduction a graph g of size q is odd graceful, if there is an injection. The purpose of this book is to provide some results in a class of. A metaheuristic approach to the graceful labeling problem. A graceful labeling of a graph g with q edges is an injective assignment of labels from 0, 1. Fibonacci and super fibonacci graceful labeling of some graphs 103 5.
In this paper we investigate strong edge graceful labeling of windmill graph. Nov 28, 2014 graceful labeling for open star of graphs ii. Gracefully labeled graphs serve as models in a wide range of applications including coding theory and communication network addressing. An example usage of graph theory in other scientific. Most of these topics have been discussed in text books.
Introductory graph theory by gary chartrand, handbook of graphs and networks. What are some real life applications of graceful and. 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. Labeling, graceful labeling, cycle, complete bipartite graph, cycle of graphs. C n denotes a cycle on n vertices and k m,n denotes. A second type, which might be called a triangular book, is the complete tripartite graph k 1,1,p. On graceful labeling of some graphs with pendant edges.
A graph which admits edge odd graceful labeling is called an edge odd graceful graph. Some of the major themes in graph theory are shown in figure 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. The windmill graphs k m n n 3 to be the family of graphs consisting of n copies of k m with a vertex in common. Edge even graceful labeling is a new type of labeling since it was introduced in 2017 by elsonbaty and daoud ars combinatoria. V 0, 1, e is called graceful if the weight of edge wuv fu.
A graph g is said to be strong edge graceful if it admits a strong edge graceful labeling. 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. Let g be an undirected graph without loops or double connections between vertices. Fuzzy sets research graphic methods set theory printer friendly 24,992,089 articles and books. If is a fixed tree with edges, then complete graph on vertices decomposes into copies of. Graceful labeling for some supercaterpillar graphs. The graceful labeling was introduced by rosa rosa 1967, p. 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.
The field of graph theory plays an important role in. Odd graceful labeling of acyclic graphs science publishing. Applications of graph labeling in communication networks. We show precisely when these labellings can also be. For detail survey of graph labeling one can refer gallian gallian 20. Applications of mathematical programming in graceful labeling of graphs. Pdf graceful labeling of some graphs and their subgraphs. The edge even graceful labeling of some triangular graphs are shown in figure 7. As we mention there the ringel conjecture and many efforts to settle it provided the reason for various graph labeling problems. Edge even graceful labeling of some graphs journal of the.
What are some good books for selfstudying graph theory. Further results on super graceful labeling of graphs. The gracefulness will get influenced by various properties of set theory. The injective mapping is called graceful if the weight of edge are all different for every edge xy. It is not the easiest book around, but it runs deep and has a nice unifying theme of studying how. 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. The field of graph theory plays an important role in various areas of pure and applied sciences. Introductory chapters present the main ideas and topics in graph theorywalks, paths and. A comprehensive introduction by nora hartsfield and gerhard ringel. In this work we introduce a new graph which is called cycle of graphs and it is denoted by cg1,g2. Odd graceful labeling of the revised friendship graphs. A graph is called graceful if it has at least one such labeling.
Jul 10, 2017 graceful labeling is one of the interesting topics in graph theory. Find the top 100 most popular items in amazon books best sellers. 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 bit of history the concept of graceful labeling was initially used to attack the problem of the decomposition of graphs. The notation and terminology used in this paper are taken from gallian 9. Keywords graph theory, odd graceful labeling, friendship graphs. A graph which admits a graceful labeling is called a. Concluding remarks we introduced here a new graph is called cycle of graphs. 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, colouring of.
Chapter 5 fibonacci graceful labeling of some graphs. It is easily shown that every path has a graceful labelling, however, in this paper we show that given almost any path p with n vertices then for every vertex email protected. 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. Graph labeling has applications in many areas, i would like to know the application of graceful labeling view which tools are used for drawing graphs in graph theory. Graceful, harmonious and magic type labelings relations and. In section 4, certain new aspects of applications of antimagic, inner magic, and inner antimagic labelings and other kinds of labelings given in refs. This labeling was originally introduced in 1967 by rosa. A graph is called d graceful if it has a d graceful labeling, where the set d is called a graceful set of g. The book includes number of quasiindependent topics.
We discussed here graceful labeling for cycle of graphs. There are several types of graph labeling and a detailed survey is found in 4. A graph is called graceful if it has a graceful labeling. The field of graph theory plays vital role in various fields.
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