In this paper we investigate difference labeling on a gear graph, ladder, fan graph, friendship graph, helm graph, wheel graph keywords. While there are many different graph labeling techniques, in this. An antimagic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the set of integers 1, 2, q such that the vertex sums are pairwise distinct, where. An example usage of graph theory in other scientific fields. However, its core ideas can be traced back to the work of founding french. 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. A graph with such a function defined is called a vertexlabeled graph. We also study directed graphs or digraphs d v,e, where the edges have a direction, that is, the edges are ordered. Pdf vertex odd mean and even mean labeling of some. Our work focuses on the adjacency labeling schemes for the class of trees, which are often used to.
Let v g be the vertex set and e g be the edge set of graph g. Graphs with alabelings have often proved useful in the development of the theory of graph decompositions. Introduction all graphs in this paper are simple finite. A graph g with p vertices and q edges is a mean graph if there is an injective function f from the vertices of g to 0,1,2. Apr 25, 2016 part bipartite graph in discrete mathematics in hindi example definition complete graph theory duration. General definitions of cycles, wheels, fans, friendship graphs, magic labeling, vertex magic total labeling, edge magic total labeling, total magic labeling are as follows. 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. E be a simple, undirected and nite graph with p vertices and q edges. Pdf a dynamic survey of graph labeling semantic scholar. The field of graph theory plays vital role in various fields. One of the important areas in graph theory is graph labeling used in many applications like coding theory, xray crystallography, radar, astronomy. 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.
Super vertex mean labeling of cycles through different ways scielo. More generally, l,f is a distance labeling scheme for the graph family g if it is a distance labeling for every graph g. The electronic journal of graph theory and applications ejgta is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer. 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. Handbook of research on advanced applications of graph theory in modern society, 5170. Construct vertexedge graph models involving relationships among a finite number of elements. In the intervening years dozens of graph labelings techniques have been studied in over papers. Labeled graphs are becoming an increasingly useful family of. In this paper an analysis is made on union of graphs are prime cordial labeling. Applications of graph labeling in communication networks. This paper provides insights into some aspects of the possibilities and role of mind, consciousness, and their relation to mathematical logic with the application of problem solving in the fields of psychology and graph theory. Introduction to graceful graphs 2 acknowledgment i am deeply indebted to my late supervisor prof. However, without proper labeling, the graph wont make sense.
Sep 25, 2015 the concepts of graph labeling began about 50 years ago, and have been research topics for many mathematicians all over the world. Introduction to graceful graphs 5 wn w is a wheel obtained from the cycle cn rn r is a crown with 2n edges hn h is a helm with 3n edges pn p is a path or snake of length n dn m d is a dragon obtained. Chemical graphs were rst used in the later eighteenth century as the basic. A social role is a set of expectations we have about a behavior. Square difference labeling, square difference graph. Raziya begam tree with three vertices and s2 a star on three vertices then t3 s2 is formed as follows. Theory and applications labeled graphs are becoming an increasingly useful family of mathematical models for a broad range of applications. The notes form the base text for the course mat62756 graph theory. They contain an introduction to basic concepts and results in graph theory, with a special emphasis put on the networktheoretic. Chemical graphs were rst used in the later eighteenth century as the basic understanding of matter and particles were being discovered. An introduction to graph theory and network analysis with. On antimagic labeling for graph products sciencedirect.
E to be a tuple, where v is a set of vertices or nodes and e, a set of edges, is a subset of v v. In general, all the graphs are not prime, it is very interesting to investigate graph families which admit prime labelling. Lecture notes semester 1 20162017 dr rachel quinlan school of mathematics, statistics and applied mathematics, nui galway march 14, 2017. Most of the graph labeling techniques trace their origin to graceful labeling introduced independently by rosa3 and golomb4 which is defined as follows. Graph theory, labeling of graphs, enumeration of graphs are just to name a few. A graph which admits prime cordial labeling is called prime cordial graph. For all other terminology and notations we follows harary harary. Many problems of graph theory consist in finding a vertex or an edge labeling for a graph satisfying certain properties. Rosa ga66, for instance, has shown that if g is a graph with 4 edges and has an a. It is important to note that the function f, responsible of the distance computation, is independent of g. 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. Labeling theory also referred to as societal reaction theory analyzes how social groups create and apply definitions for deviant behavior.
We follow the standard notations and terminology of. The approach examines how deviant labels emerge, how some social groups develop the power to impose deviant labels onto selected others, and the consequences of being labeled deviant. This report survey the smarandache system, labeling graphs and others in the classical graph theory. A general reference for graph theoretic notations is 3. This theory is most commonly associated with the sociology of crime since labeling someone unlawfully deviant can lead to poor conduct. Labeling, covering and decomposing of graphs citeseerx. This section is based on graph theory, where it is used to model the faulttolerant system. Somasundaram and ponraj 4 have introduced the notion of mean labeling of 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. The central question of spectral graph theory asks what the spectrum i.
In this paper we prove that the split graphs of k1,n and bn,n are prime cordial graphs. Labeling theory states that people come to identify and behave in ways that reflect how others label them. The labeling of the vertices respectively edges is injective if distinct vertices respectively edges have distinct labels. Describe a vertexedge graph using an adjacency matrix. Thomassen, kuratowskis theorem, journal of graph theory 5 1981, 225241.
Qualitative labelings of graph elements have inspired research in diverse fields of human enquiry such as conflict resolution in social psychology. The idea of labeling theory flourished in american sociology during the 1960s, thanks in large part to sociologist howard becker. A vertex labeling of a graph g is an assignment f of labels to the vertices of g that induces for each edge xy a label depending on the vertex labels fx and fy. Edgemagic labeling of some graphs 49 figure 4 super edgemagic labelings of merge graphs theorem 3.
Z, in other words it is a labeling of all edges by integers. Such a synthesis of labeling theory and personal construct theory will not only go a long way towards answering the major criticisms leveled against labeling theory but will provide a. There is a part of graph theory which actually deals with graphical drawing and presentation of graphs, brie. He introduced me to the world of graph theory and was always patient, encouraging and resourceful. In this project, we study certain types of graph coloring and graph labeling techniques and and their applications to various theoretical and. It took a hundred years before the second important contribution of kirchhoff 9 had been made for the analysis of electrical networks. A graph with difference labeling defined on it is called a labeled graph. In this paper we investigate prime labeling for some fan related graphs. This work aims to dispel certain longheld notions of a severe psychological disorder and a wellknown graph labeling conjecture. It is very interesting to investigate graphs which admit power 3 mean labeling. Labeling theory concerns itself mostly not with the normal roles that define our lives, but with those very special roles that society provides for deviant behavior, called deviant roles, stigmatic roles, or social stigma. For many, this interplay is what makes graph theory so interesting. A super vertex mean labeling f of a p,q graph g v,e is defined as. Abstractin this paper, we introduced energy of fuzzy labeling graph and its denoted by ef.
A study on the product setlabeling of graphs arxiv. Conclusion the study of labeled graph is important due to its diversified applications. We discuss concepts of graph theory and how they apply to this papers approach to this project. Qualitative labelings of graph elements have inspired research in diverse fields of human enquiry such as conflict resolution in social psychology, electrical circuit theory and energy crisis etc. Some new standard graphs labeled by 3total edge product. Although underscoring the salience of formal labeling, the. Part bipartite graph in discrete mathematics in hindi example definition complete graph theory duration. Social network analysis sna is probably the best known application of graph theory for data science.
To form the graph t5 sn merge the vertex v1 of sn with the vertex d of t5 and label it v1. 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. Rosa, on certain valuations of the vertices of a graph, theory of graphs. Pdf graceful labeling of some graphs iir publications. Apr 19, 2018 graph theory concepts are used to study and model social networks, fraud patterns, power consumption patterns, virality and influence in social media. The theory assumes that although deviant behavior can initially stem from various causes and conditions, once individuals have been labeled or defined as deviants. Formally, given a graph g v, e, a vertex labelling is a function of v to a set of labels.
A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. A function f is called harmonious labeling of graph g if f. Further we prove that the wheel graph wn admits prime cordial labeling for n. 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. T5 sn is super edge magic, where t5 is a tree on five vertices and sn is. A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. A scottish chemist, william cullen, rst termed them as a nity diagrams in lecture notes to represent. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of. Here, the computer is represented as s and the algorithm to be executed by s is known as a. Conferenceseminar papers in all areas of graph theory will be published as a special issue. V 0, 1, 2,,q1 is injective and the induced function f. Cycle is a graph where there is an edge between the adjacent. In this chapter we discuss several interrelated graph labeling problems.
Electronic journal of graph theory and applications ejgta. Graph labelings were first introduced in the late 1960s. In a weighted graph, the weight of a path is the sum of the weights of the edges traversed. Pdf analysis of various graph labeling techniques from. If is a regular graph with 3, then is not power 3 mean graph. Research paper harmonious labeling of certain graphs. Jul 12, 2006 handbook of research on advanced applications of graph theory in modern society, 5170. A labeling of a graph g is an assignment of labels either to the vertices or edges. A difference labeling of g is an injection f from v to the set of non. Labeling theory provides a distinctively sociological approach that focuses on the role of social labeling in the development of crime and deviance. A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graphs are an excellent way to make a visual representation of data that have been collected. Umbrella graph, p nqs n graph, c nq sn graphs are square difference graphs. A labeling is an assignment of labels to edges, vertices, or both edges and vertices of a graph.
Yellen, graph theory and its applications, crc press, boca raton, 1999. General definitions of cycles, wheels, fans, friendship graphs, magic labeling, vertex magic total. Graph theory is one of the topics in an area of mathematics. Keywords friendship graph, harmonious labeling, cordial labeling, distance. 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 labeling is an edge labeled graph. In this paper we investigate mean labeling of shadow graph of bistar and. Vizings theorem vizings theorem states that for any graph g, g. Therefore, make sure you label the xaxis and yaxis and title your graph so it can be understood by people without having to ask what it represents. A dynamic survey of graph labeling the electronic journal of. Any graph labeling will have the following three common characteristics. Mathematical models for a broad range of applications. It is used in clustering algorithms specifically kmeans. University of south carolina graph labeling with distance.
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