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. This second part is probably more accessible to readers i and it can be read separately. The second part of my examination was made in the spring of 1976. In this paper we investigate prime labeling for some fan related graphs. 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 multivariable theory of criminal behavior, one which can take both subjective and objective factors into consideration. Normally, this subject is presented in terms of the. If f is an injection from the vertices of g to the set 2,4,6. The standard notations and terminology are as in 2. Qualitative labelings of graph elements have inspired research in diverse fields of human enquiry such as conflict resolution in social psychology. In this paper we investigate mean labeling of shadow graph of bistar and comb and splitting graph of comb. In this section we introduce neutrosophic labeling graph, neutrosophic labeling subgraph, connectedness in neutrosophic labeling graph, neutrosophic partial cut node and neutrosophic partial bridge and investigated some of the properties with suitable examples. In this paper, we investigate super geometric mean labeling of some cycle related graphs. 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. Define, where du denotes the degree of u and nu denotes the open neighborhood of u.
In this paper the prime labeling of certain classes of graphs are discussed. A more elaborate definition is due to azriel rosenfeld 8 who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graph in. Further we prove that the wheel graph wn admits prime cordial labeling for n. Labeling of graphs plays an important role in application of graph theory in neural networks, coding theory, circuit analysis etc. Vertex odd mean and even mean labeling of some graphs. Merge graph introduction in this paper, by a graph we mean only finite simple undirected graphs. He introduced me to the world of graph theory and was always patient, encouraging and resourceful. In this paper, we study the existence of harmonious labeling for the corona graphs of a cycle and a graph and for the corona graph of and a tree. In general, all the graphs are not prime, it is very interesting to investigate graph families which admit prime labelling. 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. A graph consists of some points and lines between them. A graph, which admits an even mean labeling, is said to be even mean graph. Our objective here is to supplement this viewpoint with a graphtheoretic approach, which provides a useful visual representation of the process.
Conferenceseminar papers in all areas of graph theory will be published as a special issue. Revathi department of mathematics seethalakshmi ramaswami college tiruchirappalli 620002. One important problem in graph theory is graph coloring or graph labeling. Somasundaram and ponraj 4 have introduced the notion of mean labeling of graphs. A classical method for finding a lower bound on the radio klabeling number of a graph is to use the following relation with another graph parameter called the upper traceable number. Originating in howard beckers work in the 1960s, labeling theory explains why peoples behavior clashes with social norms. The labeling of the vertices respectively edges is injective if distinct vertices respectively edges have distinct labels. Nevertheless, until now almost nothing is known about games related to graph labeling. In this paper we introduce a new labeling called dlucky labeling and study the same as a vertex coloring problem.
Labeled graphs form useful mathematical models for a wide range of applications such as coding theory, xray crystallography. Labeling definition of labeling by the free dictionary. However, its core ideas can be traced back to the work of founding french sociologist emile durkheim. For the basics of graph theory concepts and notations refer to harary4 and douglas b. We also discuss prime labeling in the context of some graph operations namely fusion and duplication in fan fn keywords. In a weighted graph, the weight of a path is the sum of the weights of the edges traversed. There is a part of graph theory which actually deals with graphical drawing and presentation of graphs, brie. Z, in other words it is a labeling of all edges by integers. It is of interest to note that hgraph which is a 3 regular graph satisfy prime labeling. 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. Vertex odd mean and even mean labeling of some graphs n. Introduction to graceful graphs 2 acknowledgment i am deeply indebted to my late supervisor prof. A graph which admits super geometric mean labeling is called super geometric mean graph. Yellen, graph theory and its applications, crc press, boca raton, 1999.
American sociologist george herbert meads theory framing social construction of the self as a process involving interactions with others also influenced its development. The field of graph theory plays vital role in various fields. A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. There are many kinds of graph labeling such as graceful labeling, magic labeling, prime labeling, and other different labeling techniques. It took a hundred years before the second important contribution of kirchhoff 9 had been made for the analysis of electrical networks. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph. 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 graph which admits prime labeling is called a prime graph. 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.
In this paper we investigate prime labeling for some helm related graphs. Chapter 17 graphtheoretic analysis of finite markov chains. Here we prove that the graphs like flower fln, bistar bn,n, square graph of bn,n, shadow graph of. In labeling valuation or numbering of a graph g, we associate distinct nonnegative integers to the vertices of g as vertex labels vertex values or vertex numbers in such a way that each edge receives a distinct positive integer as an edge label edge value or edge number depending on the vertex labels of vertices which are. 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. V g n be a labeling of the vertices of a graph g by positive integers. A new graph g1 is constructed by identifying fusing two vertices u and v by a single vertex x in such that every edge which was incident with either u or v in g now incident with x in g. If the integers are the first q positive integers, where q is the number of edges, the graph and the labelling are called supermagic. 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. Raziya begam tree with three vertices and s2 a star on three vertices then t3 s2 is formed as follows. A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions5. Labeling problem is a wellstudied problem due to its wide applications, especially. Labeling theory also referred to as societal reaction theory analyzes how social groups create and apply definitions for deviant behavior.
It took a hundred years before the second important contribution of kirchhoff 9 had been made for the analysis of. Part bipartite graph in discrete mathematics in hindi example definition complete graph theory duration. A function f is called an even mean labeling of a graph g with p vertices and q edges. Applications of graph labeling in communication networks. Graph is a mathematical representation of a network and it describes the relationship between lines and points. In this paper we prove that the split graphs of k1,n and bn,n are prime cordial graphs. The first definition of fuzzy graph was introduced by kaufmann 1973, based on zadehs 11 fuzzy relations 1971.
A graph g with p vertices and q edges is a mean graph if there is an. In sociology, labeling theory is the view of deviance according to which being labeled as a deviant leads a person to engage in deviant behavior. Graph theory is a branch of mathematics started by euler 45 as early as 1736. A difference labeling of g is an injection f from v to the set of non negative integer with weight function on e given by for every edge in g. The length of the lines and position of the points do not matter. Theory and applications labeled graphs are becoming an increasingly useful family of mathematical models for a broad range of applications. An outline of the results contained in all the chapters is given in the introduction. The term not defined here are used in the sense of harary 3.
A magic graph is a graph whose edges are labelled by positive integers, so that the sum over the edges incident with any vertex is the same, independent of the choice of vertex. A graph with such a labeling is an edge labeled graph. Label definition is a slip as of paper or cloth inscribed and affixed to something for identification or description. A graph with edges is said to be harmonious, if there is an injection from the vertices of to the group of integers modulo such that when each edge is assigned the label mod, the resulting edge labels are distinct. The square divisor cordial labeling is a variant of cordial labeling and divisor cordial labeling. Pdf basic definitions and concepts of graph theory. 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. The idea of labeling theory flourished in american sociology during the 1960s, thanks in large part to sociologist howard becker.
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