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