A comprehensive introduction by nora hartsfield and gerhard ringel. The graceful labeling was introduced by rosa rosa 1967, p. The injective mapping is called graceful if the weight of edge are all different for every edge xy. The graceful labeling of the graph then corresponds to the. A bit of history the concept of graceful labeling was initially used to attack the problem of the decomposition of graphs. Odd graceful labeling of acyclic graphs science publishing. A graph with such a labeling is an edge labeled graph. Gao 6 in which he studied the odd graceful labeling of union of any number of paths and union of any number of stars, we have determined odd graceful labeling for some other union of graphs. In this paper the prime labeling of certain classes of graphs are discussed. Z, in other words it is a labeling of all edges by integers.
For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph. It covers all the topics required for an advanced undergrad course or a graduate level graph theory course for math, engineering, operations research or. 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. 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. The graph labeling model and its application to the problem of edge linking. Applications of graph labeling in communication networks. A graph g is said to be strong edge graceful if it admits a strong edge graceful labeling. Rosa a 1967 on certain valuations of the vertices of a graph. A labeled graph g which can be gracefully numbered is said to be graceful. Labeling the nodes of g with distinct nonnegative integers and then labeling the e edges of g with the absolute differences between node values, if the graph edge numbers run from 1 to e, the graph g is gracefully numbered. A graph with such a function defined is called a vertexlabeled graph. Formally, given a graph g v, e, a vertex labelling is a function of v to a set of labels.
The upperright and lowerleft squares of the adjacency matrix thus always contain a 1, shown as a black square here. Covers design and analysis of computer algorithms for solving problems in graph theory. I used this book to teach a course this semester, the students liked it and it is a very good book indeed. The study of graceful labeling of graphs with pendant edges is given by christian barrientos 14. The handbook of graph theory is the most comprehensive singlesource guide to graph theory ever published. Keywords graph theory, odd graceful labeling, friendship graphs. The name graceful labeling was coined later by golomb. A function f is called graceful labeling of a graph g v. Edge odd graceful labeling of some path and cycle related.
Most of these topics have been discussed in text books. Further results on super graceful labeling of graphs. Identify the edges of with suitable edges of, where q eg 3. Graceful labeling i for a connected graph g with q edges, a vertex labeling f. Some of the major themes in graph theory are shown in figure 3. Each vertex and each edge of is rotated times from the original position. A graph is called graceful if it has at least one such labeling. Includes a collection of graph algorithms, written in java, that are ready for compiling and running. Edge even graceful labeling of polar grid graphs mdpi. Introduction a graph g of size q is oddgraceful, if there is an injection. The book includes number of quasiindependent topics. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
Graceful labeling is one of the interesting topics in graph theory. The field of graph theory plays vital role in various fields. Each time the count of lattice points decreases by unity as we move down by one row till. Introductory graph theory by gary chartrand, handbook of graphs and networks. Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to practical problems. Gracefully labeled graphs serve as models in a wide range of applications including coding theory and communication network addressing. There are many kinds of graph labeling such as graceful labeling, magic labeling, prime labeling, and other different labeling techniques. A graph g with q edges is said to be oddgraceful if there is an injection f. 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.
A generalized theta graph consisting of n internal disjoint paths. Concluding remarks we introduced here a new graph is called cycle of graphs. Square graceful labeling of some graphs open access journals. A labeling graph g which can be gracefully numbered is said to be graceful. The notation and terminology used in this paper are taken from gallian 9. For anyone interested in learning graph theory, discrete structures, or algorithmic design for graph. Graceful labeling of arbitrary supersubdivision of grid. A graph g with q edges and p vertices is said to be edge graceful if there exists a bijection f from the. It is of interest to note that hgraph which is a 3 regular. Bestselling authors jonathan gross and jay yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theoryincluding those related to algorithmic and optimization approach. On graceful labeling of some graphs with pendant edges. In between, the authors discuss the history and the mathematical concepts at an elementary level, hoping that the book may serve as a first textbook of graph theory. V 1,2, n for every vertex such that each edge is labeled a distinct integer 1,2, n. An algorithm to generate all the labeled spanning trees in a complete graph is developed and modified to generate all graceful spanning trees.
A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed. This is a very good introductory book on graph theory. A graceful labeling of a graph g with q edges is an injective assignment of labels from 0, 1. Let be a graph obtained by replacing each vertices of except the apex vertex by the graph let is the. Discusses applications of graph theory to the sciences. 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. 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. Odd graceful labeling of the revised friendship graphs. Agraph which admits graceful labeling is called graceful graph. Let g be an undirected graph without loops or double connections between vertices.
Doublewheel graphs are graceful cornell university. Some topics in graph theory the purpose of this book is to provide some results in a class of problems categorized as graph labeling. Fibonacci and super fibonacci graceful labeling of some graphs 103 5. Let g v, e be a finite, simple and undirected graph. Edge even graceful labeling on circulant graphs with. Subbiah lecturer sg in mathematics, periyar evr college, trichy 620 023, india email. The labeling pattern is demonstrated by means of illustrations, which provide better understanding of derived results. Mehendale sir parashurambhau college, pune411030, india. This book teaches basic graph theory through excerpts from original papers in english translation.
There are different types of labeling such as graceful labeling, magic labeling, edgegraceful labeling, prime labeling, radio labeling, harmonious labeling etc. Graceful labeling for open star of graphs by invention. In this paper, we have constructed an edge even graceful labeling on. Research in graph theory has lead to one of the important area called labeling of graphs. Graph labeling is an important area of research in graph theory.
Graceful labeling of generalized theta graphs springerlink. A graph g is called graceful if it has a graceful labeling. As we mention there the ringel conjecture and many efforts to settle it provided the reason for various graph labeling problems. Abstract we define so called ndelta lattice containing n1 lattice points in first topmost row, n2 lattice points in second row, and so on. In this paper we investigate strong edge graceful labeling of windmill graph. In this paper we introduced fuzzy vertex gracefulness and discussed to wheel graphs and fan graphs. 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. Fuzzy vertex graceful labeling on wheel and fan graphs. A graceful labeling of a graph g is a mapping of function f. Chapter 5 fibonacci graceful labeling of some graphs. Introduction a graph g of size q is odd graceful, if there is an injection. Several authors worked on graceful labeling, odd graceful labeling, even graceful labeling, super graceful labeling and skolem graceful labeling. A graph g with q edges is said to be odd graceful if there is an injection f. On sequential labelings of graphs grace 1983 journal of.
Nov 28, 2014 graceful labeling for open star of graphs ii. Pdf graceful labeling of some graphs and their subgraphs. Graceful labeling for corona and flower graph aip publishing. I such a labeling is called graceful if the edges are labeled 1. 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. 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 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. Read, highlight, and take notes, across web, tablet, and phone. This labeling was originally introduced in 1967 by rosa. If you dont want to be overwhelmed by doug wests, etc. 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.
We discussed here graceful labeling for cycle of graphs. Each diagonal parallel to the main diagonal of must have exactly one black square for the graph to be graceful. There are several types of graph labeling and a detailed survey is found in 4. A new graceful labeling for pendant graphs springerlink.
Contents 1 introduction 3 2 notations 3 3 preliminaries 4 4 matchings 5 connectivity 16 6 planar graphs 20 7 colorings 25 8 extremal graph theory 27 9 ramsey theory 31 10 flows 34 11 random graphs 36 12 hamiltonian cycles 38 references 39. Abstract a method to obtain all possible graceful spanning trees in a complete graph is proposed. Some labeling with variations in graceful theme are also. A complete bipartite graph is a bipartite graph such that two vertices are adjacent if and only if they are in different partite sets. A graph g is said to be edgegraceful if it admits an. 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. 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.
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