Cahit3 introduced cordial labeling of graphs and derived various results on cordial graphs. A labeling or numbering of a graph g with q edges is an assignment of labels to the vertices of g that induces for each edge uv a labeling depending on the. A graph g which admits prime labeling is called a prime graph. In this paper i investigate prime labeling for some special graph namely heawood graph. Prime labeling, heawood graph, duplication,switching. We investigate prime labeling for some graphs resulted by identifying any two vertices of some graphs. He introduced me to the world of graph theory and was always patient, encouraging and resourceful. A graph g with n vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceeding n such that the labels of each pair of adjacent vertices are relatively prime. Duplication of a vertex of a graph g produces a new graph g 1 by adding a vertex with. A graph labeling is an assignment of labels to edges, vertices or both. This work is a nice combination of graph theory and elementary number theory. A graph which admits prime cordial labeling is called prime cordial graph.
Graph obtained by identifying a rim vertex of w 8 with an end vertex of p 6 and its prime labeling. Conferenceseminar papers in all areas of graph theory will be published as a special issue. A graph on n vertices is said to admit a prime labeling if we can label its vertices with the first n natural numbers such that any two adjacent vertices have relatively prime labels. Applications of graph labeling in communication networks. The notion of prime labeling was originated by entringer and was discussed in a. It contains three types of vertices, an apex of degree 2n, n vertices of degree 4 and n vertices of degree 2. The aim of journal of graph labeling is to bring together original and significant research articles in different areas of graph labeling and graph coloring. Formally, given a graph g v, e, a vertex labelling is a function of v to a set of labels.
A graph with vertex set v is said to have a prime labeling if its vertices are. Introduction all graphs in this paper are simple, finite, connected and undirected. Abstracta graph, with n vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceed n such that the label of each pair of adjacent vertices are relatively prime. Then a prime labeling ensures that when there is a change of guard at one station, there is not simultaneously a change of guard at all the adjacent stations, until the lcm of the labels in the neighborhood is reached. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph. Nov 26, 2018 a graph g is prime if the vertices can be distinctly labeled with the integers \1,2, \ldots,vg\ so that adjacent vertices have relatively prime labels. Moreover we prove that w n is a strongly prime graph for every even integer n. A graph which admits prime cordial labeling is called a prime cordial graph. Square difference prime labeling of some planar graphs. Pdf prime labelling of some special graphs top journal. Prime labeling of families of trees with gaussian integers.
In this paper we prove that some cycle related graphs are neighborhoodprime. The field of graph theory plays vital role in various fields. Graph labeling, square sum, greatest common incidence number, prime labeling 1. Graph labeling is an important area of research in graph theory. P2 with the value of 1 assigned to the top left vertex of the graph is not a prime labeling. A graph which admits neighborhood prime labeling is called a neighborhood prime graph. The simplest example for the talk is the tetrahedron k 4. Further we prove that the wheel graph wn admits prime cordial labeling for n. In this paper we prove that the split graphs of k1,n and bn,n are prime cordial graphs. Gallians survey paper on graph labelings claims one exists and cites fu and huangs on prime labelling, which in turn cites an unpublished paper for this result. Prime labeling for duplication of graph elements in k e. The concept of prime cordial labeling was introduced by sundaram 5 et al.
Prime labeling to brush graphs international journal of. Strongly prime labeling for some graphs international journal of. Qualitative labelings of graph elements have inspired research in diverse fields of human enquiry such as conflict resolution in social psychology. A coprime labeling of a simple graph of order n is a labeling in which adjacent vertices are given relatively prime labels, and a graph is prime if the labels used. Prime labeling for some helm related graphs open access. Prime cordial labeling for some cycle related graphs. In this paper we prove that some cycle related graphs are neighborhood prime. For many, this interplay is what makes graph theory so interesting. Prime labeling of grotzch graph mathematics journal, ijmtt. Yellen, graph theory and its applications, crc press, boca raton, 1999.
Graph labeling is one of the fascinating areas of graph theory with wide ranging applications. A graph with such a function defined is called a vertexlabeled graph. 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. An affirmative answer to this interesting number theory question implies that all. In this paper the prime labeling of certain classes of graphs are discussed. An enormous body of literature has grown around in graph labeling.
Graphs which admit a total prime labeling are called total prime graph. What are primes in graphs and how many of them have a given length. A graph which admits prime labeling is called a prime graph. In this paper we investigate prime labeling for k n e where e is an edge.
Keywordsprime labeling, prime graph, brush graph, duplication, fusion, switching. We also provide evidence to support a conjectured classification for the. Murugesan2 have introduce the concept of 3c n, path n, star graph and complete graph are 3equitable prime cordial labeling. On the prime labeling of generalized petersen graphs p n. The symbol vg and eg denotes the vertex set and edge set of a graph g. In 5 proved that the path p n on n vertices is a prime graph. If c0 n be the graph obtained by duplicating a vertex by an edge in cycle cn then let v1, v2. 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. On neighbourhood prime labeling of certain classes of graphs. A graph g with n vertices is said to admit prime labeling if its vertices can be labeled with distinct. A graph g v, e with n vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceeding n such that the labels of each pair of adjacent. A graph with vertex set v is said to have a prime labeling if its vertices are labeled with distinct integer 1,2,3 such that for edge the labels assigned to and are relatively prime.
A prime cordial labeling of a graph with the vertex set is a bijection such that each edge is assigned the label 1 if and 0 if. Properties of this labeling are studied and we have proved that paths p n, star k 1,n, bistar, comb, cycles c n where n is even, helm h n, k 2,n, t c 3 and fan graph are total prime graph. V g 1,2,p is called a prime labeling if for each edge euv, gcd f u, f v1. A graph g v, e with n vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceeding n such that the labels of each pair of adjacent vertices are relatively prime. As 3equitable prime cordial labeling is extension of prime cordial labeling and many papers published on it. The graph which admits prime labeling is called a prime graph. The square divisor cordial labeling is a variant of cordial labeling and divisor cordial labeling.
Graph labeling, prime labeling, square difference, prime graphs, planar graphs. Mominul haque department of computer science and engineering shahjalal university of science and technology sylhet3114, bangladesh. We also introduce the concept of strongly prime graph and prove that the graphs cn, pn, and k1,n are strongly prime graphs. A difference labeling of g is an injection f from v to the set of non. A graph with vertex set v is said to have a prime labeling if its vertices are labeled with distinct integers the labels assigned to x and y are relatively prime. The helm graph is a labeled graph with common weight decomposition. By a prime labeling, we mean a way to label the n vertices with the integers 1 to n such that each pair of adjacent vertices is relatively prime.
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. A graph with such a labeling is an edge labeled graph. Introduction to graceful graphs 2 acknowledgment i am deeply indebted to my late supervisor prof. On the prime labeling of generalized petersen graphs pn,3 1 kh. 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. There is a part of graph theory which actually deals with graphical drawing and presentation of graphs, brie. R, graph theory and applications, northholland, newyork, 1976.
In this paper we have proved that some classes of graphs such as the flower pot, coconut tree, umbrella graph, shell graph, carona of a hell graph,s carona of a wheel graph, carona of a ear graphg, butterfly graph, two copies of cycle. Square sum prime labeling of some path related graphs. All graphs in this paper are finite and undirected. Prime labeling, prime graph, generalized petersen graph 1 introduction. A graph with vertex set v is said to have a prime labeling if its vertices are labeled with distinct integer 1,2,3 such that for edge xy the labels assigned to x and y are relatively prime. A prime labeling of a graph of order is an injective function such that for every pair of adjacent vertices and.
We also discuss prime labeling in the context of some graph operations namely fusion and duplication in fan fn keywords. In this paper we investigate prime labelling of some new graphs. In this paper we investigate prime labeling for some helm related graphs. For all other terminology and notations in graph theory we follow. In this paper, we consider when ladder graphs are prime and when the corresponding labeling may be done in a cyclic manner around.
In this paper we investigate prime labeling for some fan related graphs. Pdf some results on prime and kprime labeling researchgate. Mominul haque department of computer science and engineering. In this paper we have investigated that the grotzsch graph is a prime graph and graph operations namely, fusion, duplication and switching on grotzsch graph admits prime labeling. As all the graphs are not prime graph it is very interesting to investigate graph or graph families which admit prime labeling. A graph which satisfies the conditions of prime labeling and harmonious labeling is called a prime harmonious labeling. A primein a graph is a closed path in the graph minimizing the number of edges traversed.
In this paper an analysis is made on union of graphs are prime cordial labeling. We also discuss prime labeling in the context of some graph operations namely fusion and duplication in helm aa a aaa a a. We follow gross and yellen 4 for graph theoretic terminology and notations and 1 for elementary number theory results. Here we prove that the graphs like flower fln, bistar bn,n, square graph of bn,n, shadow graph of.
Theory and applications labeled graphs are becoming an increasingly useful family of mathematical models for a broad range of applications. We also introduce the concept of strongly prime graph and prove that the graphs c n, p n, and k 1,n are strongly prime graphs. Abstract a prime labeling of a graph g with n vertices is a labeling of the. We prove that the graphs such as flower graph f, the splitting graph of star, the bistar, the friendship graph the graph sfn,1 are prime graphs. Labeling of graph is the potential area of research and more than 1200 research papers have been published so far in past. A graph which admits a prime cordial labeling is called a prime cordial graph. The prime labeling of some cycle related graphs were discussed in 7. Thus in all the possibilities f1 admits a prime labeling for 1. Neighborhoodprime labeling of some cycle related graphs. A graph that admits a prime labelling is called a prime graph.
Pdf a graph g v, e with n vertices is said to admit prime labeling if its. A graph which admits neighborhoodprime labeling is called a neighborhoodprime graph. We introduce a new type of labeling known as total prime labeling. Z, in other words it is a labeling of all edges by integers. Moreover we prove that wn is a strongly prime graph for every even integer n. In this paper we investigate prime labeling for some graphs related to h graph, ladder graph, comb graph and also we prove that comb graphis a strongly prime graph. In this paper we have proved that some classes of graphs such as the flower pot, coconut tree, umbrella graph, shell graph. A coprime labeling of a simple graph of order n is a labeling in which adjacent vertices are given relatively prime labels, and a graph is prime if the labels used can be taken to be the. If is a prime graph with order, where is even and is a graph with order 3 then disjoint union of and is a prime graph. A graph which admits a prime harmonious labeling is called a prime harmonious graph and it is denoted by p h. We also show that the square graph of bn,n is a prime cordial graph while middle graph of pn is a prime cordial graph for n. Prime labeling for some cycle related graphs semantic scholar. Pdf some new results on prime graphs udayan prajapati. Prime labeling, prime graph, strongly prime graph, h graph, ladder graph, comb graph.