Nagarajan 1 investigate neighbourhood prime labeling for some special graphs like friendship graph, gear, ladder, triangular book and coconut tree. Applications of graph labeling in communication networks. It is not the easiest book around, but it runs deep and has a nice unifying theme of studying how. Some new results on prime graphs scientific research publishing. This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. Square difference labeling, square difference graph. Graph labeling, prime labeling, square difference, prime graphs, planar graphs. So we have to use 1 to natural numbers to label these vertices, and from 1 to there are even integers.
The systematic study of number theory was initiated around 300b. The format is similar to the companion text, combinatorics. Find the top 100 most popular items in amazon books best sellers. Some of the major themes in graph theory are shown in figure 3.
An outline of the results contained in all the chapters is given in the introduction. A prime labeling of a graph is an injective function f. 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. 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. One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science. The last three decades have witnessed an upsurge of interest and activity in graph theory, particularly among applied mathematicians and engineers. It grew out of undergraduate courses that the author taught at harvard, uc san diego, and the university of washington. The simplest example for the talk is the tetrahedron k 4. Prime labeling for duplication of graph elements in k e. Further we prove that the wheel graph wn admits prime cordial labeling for n. In this paper we investigate prime labeling for some fan related graphs. A common theme in graph labeling papers is to build up graphs that have. It took a hundred years before the second important contribution of kirchhoff 9 had been made for the analysis of electrical networks. A prime labeling of a graph of order is an injective function such that for every pair of adjacent vertices and.
Set theory, matrix maths and some calculus is a prerequisite to using the tools in this book. Nagarajan 2 investigate neighbourhood prime labeling for special graphs like friendship graph, gear, ladder, triangular book and. All unicyclic graphs have a prime vertex labeling seoud and youssef 5. The graph which admits prime labeling is called a prime graph. In general, all the graphs are not prime, it is very interesting to investigate graph families which admit prime labelling. Moreover we prove that w n is a strongly prime graph for every even integer n. In the following figures 3 and 4 prime labeling of a graph of order 5 and the prime labeling for the graph g1 obtained by identifying the vertices of with label 1 and 5 are shown. For graph theoretic terminology, we refer to harary 2. Some vertex prime graphs and a new type of graph labeling. A graph g which admits prime labeling is called a prime graph. They also show that a 2regular graph with at least two odd cycles has no vertex prime labeling. All graphs in this paper are finite and undirected. A graph which admits a prime cordial labeling is called a prime cordial graph.
Here, we investigate and prove that new results for triangular book admits prime labeling when is even and odd. Further we prove that the wheel graph wn admits prime cordial labeling. Z, in other words it is a labeling of all edges by integers. We introduce a new type of graph labeling called as lcordial labeling and show that k 1,n,path p n, c n,sc 3. Square difference prime labeling more results on path related graphs chapter 12 advances in mathematics and computer science vol. We also introduce the concept of strongly prime graph and prove that the graphs cn, pn, and k1,n are strongly prime graphs. 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 formally, given a graph, a vertex labelling is a function of to a set of labels. Moreover we prove that wn is a strongly prime graph for every even integer n. Much of the material in these notes is from the books graph theory by reinhard diestel and. Pdf some results on prime and kprime labeling researchgate. 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.
They proved that the cycle, complete graph kn, the cycle cactus, ladder and complete lattice grids are square. 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. 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. In this paper an analysis is made on union of graphs are prime cordial labeling. Yellen, graph theory and its applications, crc press, boca raton, 1999. A second type, which might be called a triangular book, is the complete tripartite graph k 1,1,p. Here we extend the idea of prime labeling to the gaussian integers, which are the complex numbers whose real and imaginary parts are both integers. In this paper we investigate some new families of vertex prime graphs. Prime vertex labelings of several families of graphs. A graph which admits prime labeling is called a prime graph. 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. This work is a nice combination of graph theory and elementary number theory.
A graph labeling is an assignment of labels to edges, vertices or both. If is an odd integer then the prism graph is not prime proof. Umbrella graph, p nqs n graph, c nq sn graphs are square difference graphs. I was thinking of any applications like scheduling etc. A graph which admits total prime labeling is called total prime graph.
Buy graph theory book online at low prices in india graph. Acknowledgement much of the material in these notes is from the books graph theory by reinhard diestel and introductiontographtheory bydouglaswest. Department of mathematics, seattle university, 901 12th avenue, seattle. Neighborhoodprime labelings of trees and other classes of graphs. We prove that the graph obtained by subdivision of pendent edges of stars, bistars, coconut trees and kite graphs are all total prime graphs. Qualitative labelings of graph elements have inspired research in diverse fields of human enquiry such as conflict resolution in social psychology. In this paper the prime labeling of certain classes of graphs are discussed. Nonplanar graphs can require more than four colors, for example this graph this is called the complete graph on ve vertices, denoted k5.
If is odd then we can use at the most even integers to label the vertices of a. A concise introduction to a fascinating field of data analytics. 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. E be a simple, undirected and nite graph with p vertices and q edges. The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. Thus in each of the possibilities the graph g under consideration admits a prime labeling. The 7page book graph of this type provides an example of a graph with no harmonious labeling. In this paper we investigate prime labeling for some helm related graphs. For all other terminology and notations we follows harary harary 1972. There are many kinds of graph labeling such as graceful labeling, magic labeling, prime labeling, and other different labeling techniques.
In the present work we investigate some classes of graphs which admit prime. A graph g is a prime distance graph if its vertices can be labeled with distinct integers in such a way that for any two adjacent vertices, the absolute difference of their labels is a prime number. The graph admitting vertex prime labeling is called as verterx prime graph. 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. Theory and applications labeled graphs are becoming an increasingly useful family of mathematical models for a broad range of applications. A difference labeling of g is an injection f from v to the set of non. Neighbourhood prime labeling on some graphs semantic scholar. What are some good books for selfstudying graph theory.
Discrete mathematics 127 1994 181186 181 northholland on prime labellings hunglin fu and kuoching huang department of applied mathematics, national chiaotung university, hsinchu, taiwan, roc received 1 october 1990 revised 5 october 1991 abstract let gv, e be a graph. The scope of graph theory if being increasingly felt because of its wide ranging applications in computer science, computer science, communication engineering and management science etc. 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. Likewise, an edge labelling is a function of to a set of labels. A primein a graph is a closed path in the graph minimizing the number of edges traversed. The symbol vg and eg denotes the vertex set and edge set of a graph g.
For a simple graph g with n vertices in the vertex set vg, a prime labeling is an assignment of the. Proof letg be a graph without cycles withn vertices and n. In this paper we investigate prime labeling for k n e where e is an edge. Acquaintanceship and friendship graphs describe whether people know each other. Prime labeling of families of trees with gaussian integers. 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. Graph theory presents a natural, readerfriendly way to learn some of the essential ideas of graph theory starting from first principles. Covers basic graph theory and then goes off into a wide range of applications and analytic tools. Many families of graphs are known to admit prime labelings such as paths, stars, caterpillars, complete binary trees, spiders, palm trees, fans, flowers, and many more.
Square difference prime labeling more results on path. Free graph theory books download ebooks online textbooks. Marcus, in that it combines the features of a textbook with those of a problem workbook. In this paper we prove that the split graphs of k1,n and bn,n are prime cordial graphs. 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 graph which satisfies the conditions of prime labeling and harmonious labeling is called a prime harmonious labeling.
Online shopping for graph theory from a great selection at books store. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph. Graph theory 81 the followingresultsgive some more properties of trees. For all other terminology and notations in graph theory i follow west 9. Most of these topics have been discussed in text books.
Thus the labeling defined above give a prime labeling. Introduction all graphs in this paper are simple finite undirected and nontrivial graph gv, e with vertex set v and the edge set e. The helm graph is a labeled graph with common weight decomposition. Thus in all the possibilities f1 admits a prime labeling for 1. Every connected graph with at least two vertices has an edge. It is a graph consisting of triangles sharing a common edge. Apr 26, 2016 the concept of a prime labeling of a graph was first developed by roger entriger and introduced in 15 by tout, dabboucy, and howalla. Graph theory has experienced a tremendous growth during the 20th century. The field of graph theory plays vital role in various fields. Diestel is excellent and has a free version available online.
A graph with such a labeling is an edge labeled graph. The function defined above gives prime labeling for. One of the usages of graph theory is to give a uni. In this paper, we show that the cubic graph on 8 vertices admits prime labeling, we also proved that the graphs obtained by merging or fusion of two vertices, duplication of an arbitrary vertex and switching of an arbitrary vertex in the cubic graph are prime. 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. On neighbourhood prime labeling of certain classes of graphs. Pdf a graph g v, e with n vertices is said to admit prime labeling if its vertices. We show that the graphs kayak paddle kpk,m,l, book graph. In this paper we derive certain general results concerning prime distance labeling. 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. In this paper, we consider when ladder graphs are prime and when the corresponding labeling may be done in a cyclic manner around. Reinhard diestel graph theory electronic edition 2000 c springerverlag new york 1997, 2000 this is an electronic version of the second 2000 edition of the above springer book, from their series graduate texts in mathematics, vol. Graph theory is also widely used in sociology as a way, for example, to measure actors prestige or to explore rumor spreading, notably through the use of social network analysis software. Under the umbrella of social networks are many different types of graphs.
The notion of prime labeling was originated by entringer and was discussed in a. Let g be an undirected graph without loops or double connections between vertices. Graph labeling is an important area of research in graph theory. A graph which admits prime cordial labeling is called prime cordial graph. 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. It is known that cycles and bipartite graphs are prime distance graphs. The concept of a neighborhood prime labeling of a graph is a variation of a prime labeling, which was developed by roger entriger and rst introduced in by tout, dabboucy, and howalla. A graph on n vertices admits a prime labeling if its vertices can be labeled with the first n natural numbers in such a way that any two adjacent vertices have relatively prime labels. 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. The square sum labeling and square sum graphs are 1 are defined and discussed by v. Any graph produced in this way will have an important property. A graph which admits a prime harmonious labeling is called a prime harmonious graph and it is denoted by p h. Square difference prime labeling of some planar graphs.
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