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. E be a simple, undirected and nite graph with p vertices and q edges. Prime vertex labelings of several families of graphs. Studies in graph theory magic labeling and related. 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. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph. Vg 1,2,p is called a prime labeling if for each edge euv, gcdfu, fv1. 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. For all other terminology and notations we follows harary harary 1972. Thus in all the possibilities f1 admits a prime labeling for 1. Aa a a the labels assigned to x and y are relatively prime. A difference labeling of g is an injection f from v to the set of non. Set theory, matrix maths and some calculus is a prerequisite to using the tools in this book.
The field of graph theory plays vital role in various fields. Immersion and embedding of 2regular digraphs, flows in bidirected graphs, average degree of graph powers, classical graph properties and graph parameters and their definability in sol, algebraic and modeltheoretic methods in. We prove that the graph obtained by subdivision of pendent edges of stars, bistars, coconut trees and kite graphs are all total prime graphs. Moreover we prove that w n is a strongly prime graph for every even integer n. Department of mathematics, seattle university, 901 12th avenue, seattle. Yellen, graph theory and its applications, crc press, boca raton, 1999. The 7page book graph of this type provides an example of a graph with no harmonious labeling. It is not the easiest book around, but it runs deep and has a nice unifying theme of studying how.
It is of interest to note that h graph which is a 3 regular graph satisfy prime labeling. A graph with such a labeling is an edge labeled graph. Around 1980 roger etringer conjectured that all trees have prime labeling which is. Prime labeling of families of trees with gaussian integers. Acquaintanceship and friendship graphs describe whether people know each other. Applications of graph labeling in communication networks.
An enormous body of literature has grown around graph labeling in the last five decades. Covering all its major recent developments it can be used both as a reliable textbook for an introductory course and as a graduate text. Every wheel graph wn is prime graph when n is odd and n. We investigate prime labeling for some graphs resulted by identifying any two vertices of some graphs. In recent years, graph theory has established itself as an important mathematical tool in a wide variety of subjects, ranging from operational research and chemistry to genetics and linguistics, and from electrical engineering and geography to sociology and architecture. V1,2,3, is called prime labelling if for each eu,v belong to e, we have gcd fu,fv1. In this paper we prove that the split graphs of k1,n and bn,n are prime cordial graphs.
A graph with such a function defined is called a vertexlabeled graph. Covers basic graph theory and then goes off into a wide range of applications and analytic tools. A graph with vertex set v is said to have a prime labeling if its vertices are labeled with distinct integers 1,2,3 aa a a such that for edge aa a a. Graph labelings were first introduced in the 1960s where the vertices and edges are assigned real values or subsets of a set subject to certain conditions. Further we prove that the wheel graph wn admits prime cordial labeling for n. Dec 11, 2009 labeling theory holds that deviance is not a quality of the act because it is the result of personality factors associated with committing deviance.
In this paper, we consider when ladder graphs are prime and when the corresponding labeling may be done in a cyclic manner around. Buy studies in graph theory magic labeling and related. Grid paper notebook, quad ruled, 100 sheets large, 8. Diestel is excellent and has a free version available online.
Z, in other words it is a labeling of all edges by integers. 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. All unicyclic graphs have a prime vertex labeling seoud and youssef 5. Covers fundamentals of different interpretations of labeling graphs. It is of interest to note that hgraph which is a 3 regular graph satisfy prime labeling. 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. Each vertex and each edge of is rotated times from the original position.
Introduction all graphs in this paper are simple finite undirected and nontrivial graph gv, e with vertex set v and the edge set e. 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. Around 1980 roger etringer conjectured that all trees have prime labeling which is not settled till today. A graph in which any two nodes are connected by a unique path path edges may only be traversed once. Pdf some results on prime and kprime labeling researchgate.
Buy studies in graph theory magic labeling and related concepts. Umbrella graph, p nqs n graph, c nq sn graphs are square difference graphs. The fourth edition of this standard textbook of modern graph theory has been carefully revised, updated, and substantially extended. Square difference labeling, square difference graph. That is, it is a cartesian product of a star and a single edge. A graph with n nodes and n1 edges that is connected. So we have to use 1 to natural numbers to label these vertices, and from 1 to there are even integers. 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. 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. From the above assignment the vertex labelings are distinct. Studies in graph theory magic labeling and related concepts. A graph which admits total prime labeling is called total prime graph. Quad ruled 4 squares per inch blank graphing paper notebook large 8.
Graph theorydefinitions wikibooks, open books for an open. Most of these topics have been discussed in text books. The notion of prime labeling was originated by entringer and was discussed in t out, a. Therefore, g admits prime labeling hence, g is a prime graph. Identify the edges of with suitable edges of, where q eg 3. A common theme in graph labeling papers is to build up graphs that have.
The 7page book graph of this type provides an example of a graph with no harmonious labeling a second type, which might be called a triangular book, is the complete. Under the umbrella of social networks are many different types of graphs. We also discuss prime labeling in the context of graph operations namely duplication in k n e. Topics include basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs. One kind, which may be called a quadrilateral book, consists of p quadrilaterals sharing a common edge known as the spine or base of the book. Some new results on prime graphs scientific research publishing. There are many kinds of graph labeling such as graceful labeling, magic labeling, prime labeling, and other different labeling techniques. A comprehensive introduction by nora hartsfield and gerhard ringel. A concise introduction to a fascinating field of data analytics. 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 notion of prime labeling was originated by entringer and was discussed in a.
A graph that admits a prime labelling is called a prime graph. A graph g which admits prime labeling is called a prime graph. Buy studies in graph theory magic labeling and related concepts book online at best prices in india on. A graph is known as graceful when its vertices are labeled from 0 to v, the size of the graph, and this labelling induces an edge labelling from 1 to e.
They contain an introduction to basic concepts and results in graph theory, with a special emphasis put on the networktheoretic circuitcut dualism. 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. Prime labeling for some helm related graphs open access. A graph in this context is made up of vertices also called nodes or points which are connected by edges also called links or lines. Introductory graph theory by gary chartrand, handbook of graphs and networks. The vital application of labeled graphs can be found in science, engineering and technology and we refer 4 for the same. Find the top 100 most popular items in amazon books best sellers. In general, all the graphs are not prime, it is very interesting to investigate graph families which admit prime labelling. For graph theoretic terminology, we refer to harary 2.
Some topics in graph theory the purpose of this book is to provide some results in a class of problems categorized as graph labeling. Nagarajan 1 investigate neighbourhood prime labeling for some special graphs like friendship graph, gear, ladder, triangular book and coconut tree. A second type, which might be called a triangular book, is the complete tripartite graph k 1,1,p. It is a graph consisting of triangles sharing a common edge. 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 rst n positive integers. 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.
Browse other questions tagged binatorics graphtheory primenumbers graphcolorings applications or ask your own question. 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. The notes form the base text for the course mat62756 graph theory. The overflow blog how the pandemic changed traffic trends from 400m visitors across 172 stack. The prime labeling for the vertices of wheel graph g is v0 1. Vaidya and shah 8 have investigated many results on this concept. Computation of narayana prime cordial labeling of book graphs. A graph which admits a prime harmonious labeling is called a prime harmonious graph and it is denoted by p h. It focuses on the linguistic tendency of majorities to negatively label minorities or those seen as deviant from norms. If is odd then we can use at the most even integers to label the vertices of a cycle.
Pdf a graph g v, e with n vertices is said to admit prime labeling if its vertices. The most interesting problem is to prove the prime tree conjecture. In this paper the prime labeling of certain classes of graphs are discussed. A prime labeling of a graph of order is an injective function such that for every pair of adjacent vertices and. Neighbourhood prime labeling on some graphs semantic scholar. A graph with maximal number of edges without a cycle. Vaidya and vihol 6 have also discussed prime cordial labeling in the context of graph operations while in 7 the same authors have discussed prime cordial labeling for some cycle related graphs. Free graph theory books download ebooks online textbooks. We consider only simple, finite, connected and undirected 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. 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. Discover delightful childrens books with prime book box, a subscription that. What are some good books for selfstudying graph theory.
I used this book to teach a course this semester, the students liked it and it is a very good book indeed. A graph with a minimal number of edges which is connected. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. Let g be an undirected graph without loops or double connections between vertices. 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. In this paper, we investigate several families of edge vertex prime labeling for triangular and rectangular book, butterfly graph, drums graph dn. The book includes number of quasiindependent topics. Graph labeling is one of the fascinating areas of graph theory with wide ranging applications. So those guards can monitor the change and ensure coverage.
If is an odd integer then the prism graph is not prime proof. This book depicts graph labelings that have led to thoughtprovoking. In the present work we investigate some classes of graphs which admit prime. 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. 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 graph which admits prime labeling is called a prime graph. A graph which satisfies the conditions of prime labeling and harmonious labeling is called a prime harmonious labeling. A graph with no cycle in which adding any edge creates a cycle. Many families of graphs are known to admit prime labelings such as paths, stars, caterpillars, complete binary trees, spiders, palm trees, fans, flowers, and. Research directions, contains ten articles, mainly survey type, on some current research areas in graph theory, namely, graceful labeling, l2,1labelling, complexity of graph labeling problems, dominations, interval graphs, matrices and graphs, colouring of labelled graphs and hypergraphs, selfcomplementary graphs, and strongly regular graphs. Some of the major themes in graph theory are shown in figure 3. Edge vertex prime labeling of some graphs malaya journal of. Applied graph theory provides an introduction to the fundamental concepts of graph theory and its applications.
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