A graceful labeling of a graph g with q edges and vertex set v is an injection f. Graphs with edgeodd graceful labelings 579 23 21 17 19 15 1 3 5 7 9 11 figure 1. Graceful labeling is one of the interesting topics in graph theory. Graph labeling was first introduced in the late 1960s. In this paper, we introduce a new fuzzy labeling technique called. Vimala2, 1ph d research scholar, mother teresa womens university, kodaikanal 2assistant professor, mother teresa womens university, kodaikanal, abstract. Graph theory, graceful graph, labeling of graphs, corona graph, odd graceful labeling. Fuzzy vertex graceful labeling on wheel and fan graphs r. Concluding remarks we introduced here a new graph is called cycle of graphs. A multiple shell is defined to be a collection of edge disjoint shells that have their apex in common. The labeling pattern is demonstrated by means of illustrations, which provide better understanding of derived results.
Further results on super graceful labeling of graphs. One of the important areas in graph theory is graph labeling of a graph g which is an assignment of. Intuitively speaking, the gracefulness property reveals a certain hidden regularity of the graph. Graceful labeling of bow graphs and shellflower graphs scia. Further results on super graceful labeling of graphs sciencedirect. May 09, 2016 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.
In particular, cycle related graphs have been a major focus of attention for nearly five decades. In this paper, we introduce a new type of labeling of a graph graph labeling techniques, in this seminar talk we will focus mainly on the three most popular graph labelings. In this chapter a new labeling technique is introduced termed as even graceful labeling. The definition of kedge graceful and keven edge graceful are equivalent to one another in the case of trees. A graceful labeling of a graph g with q edges and vertex set v is an. An algorithm to generate all the labeled spanning trees in a complete graph is developed and modified to generate all graceful spanning trees. Abstract a method to obtain all possible graceful spanning trees in a complete graph is proposed. In this paper, we introduce a new type of labeling of a graph labeling of a graph gis an assignment fof labels to the vertices of gthat induces for each edge xya label depending on the vertex labels fx and fy. E is called super edgemagic if each vertex label is in f1jvjgand the sum of the edge label plus labels of. A graph g with q edges is said to be odd graceful if there is an injection f.
Chapter 5 fibonacci graceful labeling of some graphs. A graph g is called graceful if it has a graceful labeling. A graph is said to be graceful if it admits a graceful labeling. A bit of history the concept of graceful labeling was initially used to attack the problem of the decomposition of graphs. Mehendale sir parashurambhau college, pune411030, india. More number of labeling techniques found their starting point from graceful labeling introduced by rosa 19678.
Jebesty shajila has studied the edge vertex graceful labeling 7. Keywords graph theory, odd graceful labeling, friendship graphs. On graceful labeling of some graphs with pendant edges. Recently the concept of square graceful labeling was introduced by t.
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. 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. In graph theory, an edge graceful graph labeling is a type of graph labeling. Note that we only give the vertex labels of all the given examples.
Graceful labeling of bow graphs and shell flower graphs. We discussed here graceful labeling for cycle of graphs. Com international journal of engineering research and technology keywords. Some results on gracefulness of few theta related graphs definition 2. The two best known labeling methods are called graceful and harmonious labelings. 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. Rajalakshmia subhasini, introduced fuzzy graph labeling and studied such as graceful labeling, vertex graceful labeling in some special graphs, etc.
Graceful labeling of some theta related graphs 79 2. 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. A labeled graph g which can be gracefully numbered is said to be graceful. Introduction a graph g of size q is odd graceful, if there is an injection. 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 vertex labeling is called a graceful labeling of a graph with edges if is an injection from the vertices of to the set 0, 1. The notation and terminology used in this paper are taken from gallian 9. In this paper we developed graceful conditions for fuzzy antimagic path graph and butterfly graph. We also provide alternative ways to construct classes of graceful graphs by creating matrices from the adjacency matrices of smaller graphs that induce larger graceful graphs. 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. Fuzzy vertex graceful labeling on wheel and fan graphs. Determining whether a graph has a harmonious labeling was shown to be npcomplete by auparajita, dulawat, and rathore in 2001 see 833.
Graceful labeling, super graceful labeling and super graceful graphs. Unicyclic graphs graceful algorithms graceful labeling algorithms jay bagga ball state university muncie, indiana, usa june 11, 2008 jay bagga graceful labeling algorithms. Examples of graceful labeling of graphs although numerous families of graceful graphs are known, a general necessary or sufficient condition for gracefulness has not yet been found. Odd graceful labeling of the revised friendship graphs. Edge even graceful labeling is a new type of labeling since it was introduced in 2017 by elsonbaty and daoud ars combinatoria. Other examples of graceful graphs will be shown in the next chapter. Vertex graceful labeling of some classes of graphs scielo. The graceful tree conjecture, which states that every tree graph on nvertices has some vertex labeling using the numbers 1. A graph gis called kgraceful graph if it admits a kgraceful labeling. A graph is called graceful if there exists a graceful labeling of see fig. The number of layers that all symmetrical trees are graceful, and there exists a graceful labeling which.
This is a labeling for simple graphs in which no two distinct edges connect the same two distinct vertices, no edge connects a vertex to itself, and the graph is connected. R thamizharasi, r rajeswari sathyabama university, india abstract in this paper we prove the edge graceful labeling methods on regular digraphs and characterized the. Fibonacci graceful labeling and fibonacci graceful graph. Graceful labeling for some supercaterpillar graphs. Application of labelled digraphs in protein networks for. A graph which admits odd graceful labeling is called an odd graceful graph.
A labeling graph g which can be gracefully numbered is said to be graceful. Interest in graph labeling began in mid1960s with a conjecture by kotzigringel and a paper by rosa90. Application of labelled digraphs in protein networks for medical technology. Edge graceful labeling for some cyclicrelated graphs. The authors in 3 showed edgeodd graceful labelings of graphs related to paths.
In this paper we introduced fuzzy vertex gracefulness and discussed to wheel graphs and fan graphs. Edge even graceful labeling of some graphs journal of the. On sequential labelings of graphs grace 1983 journal. A graph which admits a graceful labeling is called a graceful graph. A graph which admits graceful labelling is called graceful graph 1.
A shell graph is defined as a cycle cnwith n 3 chords sharing a common end point called the apex. Pdf graceful labeling is one of the interesting topics in graph theory. Pdf graceful labeling of some graphs and their subgraphs. Introduction in graph labeling vertices or edges or both assigned values subject to the conditions. In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with. The symbols vg and eg will denote the vertex set and edge set of a graph g. Graceful labeling of arbitrary supersubdivision of grid. In 1967 rosa 11 introduced the labeling method called. 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. Determining whether a graph has a harmonious labeling was shown to be npcomplete by auparajita, dulawat, and rathore in 2001 see 618. Fibonacci and super fibonacci graceful labeling of some graphs 103 5. 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. Uma and others published graceful labeling of some graphs and their subgraphs find, read and cite all the research you need on researchgate. Let g v, e be a finite, simple and undirected graph.
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. Odd graceful labeling of corona graph c2nk 1 author. Pdf graceful labeling for some supercaterpillar graphs. Many studies in graph labeling refer to rosas research in 1967 6.
Finally, a conjecture of frucht is shown to be wrong by exhibiting several graceful labelings of wheels in which the center label is larger than previously thought possible. We discussed here graceful labeling of some graphs obtained by complete bipartite graphs. A shell graph is defined as a cycle cnwith n 3 chords sharing a. A graph which admits a fuzzy graceful labeling is called a fuzzy graceful graph. Terms not defined here are used in the sense of harary 5. As we mention there the ringel conjecture and many efforts to settle it provided the reason for various graph labeling problems. In this paper, we obtained an edge even graceful labeling for some pathrelated graphs like y tree, the double star bn,m, the graph. K even edgegraceful labeling of some cycle related graphs. Index terms arbitrary supersubdivision, generalized cyclic snake, graceful labeling, grid graph.
The count of all possible graceful graphs in a complete graph is obtained. Uma 4, 5,6have analysed complete bipartite graphs, twigs, spiders, regular caterpillars, fire cracker graphs under the same labeling. Some labeling with variations in graceful theme are also. Also we define a kblock generalized cyclic snake in the increasing length and we prove that such graph is graceful. This labeling provides a sequential labeling of the edges from 1 to the number of edges. Introduction a graph g of size q is odd graceful, if there is an injection from vg to 0, 1, 2, 2q1 such that, when each edge xy. Odd graceful labeling of acyclic graphs science publishing. In 1967, rosa published a pioneering paper on graph labeling problems.
Rosa11 showed that the n cycle c n is graceful if and only if n. Research paper harmonious labeling of certain graphs dushyant tanna address for correspondence department of mathematics, marwadi engineering college, india abstract harmonious labeling of graph is getting lots of application in social networking, rare probability event and many more. A graceful labeling of a graph g of size q is an injective assignment of labels from the set 0,1. All graphs in this paper are finite, simple and undirected. Introduction by a graph, we mean a finite undirected graph without loops or multiple edges. The famous ringelkotzig tree conjecture 7 and many illustrious works on graceful graphs brought a tide of di. We denote here a star graph as s where r number of pendant vertices are connected to one vertex. Graceful labeling of arbitrary supersubdivision of grid graph. Obviously k,1graceful labeling and 1,1graceful labeling are kgraceful labeling and graceful labeling respectively. Any graph that can be gracefully labeled is a graceful graph. Applications of graph labeling in communication networks. Lattice path can be visually shown by starting with bottommost row containing lattice point labeled by vertex pair 1, n we join. A function fis called a graceful labeling of a graph gwith qedges if f.
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