In this paper an analysis is made on union of graphs are prime cordial labeling. 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. Some topics in graph theory the purpose of this book is to provide some results in a class of problems categorized as graph labeling. Marcus, in that it combines the features of a textbook with those of a problem workbook. A concise introduction to a fascinating field of data analytics. Prime vertex labelings of several families of graphs. If is odd then we can use at the most even integers to label the vertices of a. So we have to use 1 to natural numbers to label these vertices, and from 1 to there are even integers. Square difference prime labeling more results on path related graphs chapter 12 advances in mathematics and computer science vol. Every connected graph with at least two vertices has an edge. A common theme in graph labeling papers is to build up graphs that have.
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. 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. Graph labeling, prime labeling, square difference, prime graphs, planar graphs. We show that the graphs kayak paddle kpk,m,l, book graph. Graph labeling is an important area of research in graph theory. If is an odd integer then the prism graph is not prime proof. The field of graph theory plays vital role in various fields. A graph labeling is an assignment of labels to edges, vertices or both. 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. Introduction all graphs in this paper are simple finite undirected and nontrivial graph gv, e with vertex set v and the edge set e.
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. Find the top 100 most popular items in amazon books best sellers. 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. Prime labeling of families of trees with gaussian integers. Graph theory 81 the followingresultsgive some more properties of trees. 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. 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. 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. Some of the major themes in graph theory are shown in figure 3. In this paper we derive certain general results concerning prime distance labeling. It is a graph consisting of triangles sharing a common edge.
The simplest example for the talk is the tetrahedron k 4. All unicyclic graphs have a prime vertex labeling seoud and youssef 5. 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. A primein a graph is a closed path in the graph minimizing the number of edges traversed. A graph which admits a prime harmonious labeling is called a prime harmonious graph and it is denoted by p h. 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. Let g be an undirected graph without loops or double connections between vertices.
I was thinking of any applications like scheduling etc. Z, in other words it is a labeling of all edges by integers. In this paper the prime labeling of certain classes of graphs are discussed. One of the usages of graph theory is to give a uni.
It grew out of undergraduate courses that the author taught at harvard, uc san diego, and the university of washington. Umbrella graph, p nqs n graph, c nq sn graphs are square difference graphs. For all other terminology and notations in graph theory i follow west 9. Theory and applications labeled graphs are becoming an increasingly useful family of mathematical models for a broad range of applications. Thus the labeling defined above give a prime labeling. 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. 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. Square difference prime labeling more results on path. Neighborhoodprime labelings of trees and other classes of graphs. This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. The last three decades have witnessed an upsurge of interest and activity in graph theory, particularly among applied mathematicians and engineers.
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. 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. Some vertex prime graphs and a new type of graph labeling. 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. The dots are called nodes or vertices and the lines are called edges. Further we prove that the wheel graph wn admits prime cordial labeling.
The 7page book graph of this type provides an example of a graph with no harmonious labeling. 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. 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. We prove that the graph obtained by subdivision of pendent edges of stars, bistars, coconut trees and kite graphs are all total prime graphs. This work is a nice combination of graph theory and elementary number theory.
Much of the material in these notes is from the books graph theory by reinhard diestel and. Department of mathematics, seattle university, 901 12th avenue, seattle. 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. A graph which admits total prime labeling is called total prime graph. All graphs in this paper are finite and undirected. Free graph theory books download ebooks online textbooks. Qualitative labelings of graph elements have inspired research in diverse fields of human enquiry such as conflict resolution in social psychology. 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. Prime labeling for duplication of graph elements in k e. What are some good books for selfstudying graph theory. Diestel is excellent and has a free version available online.
Graph theory presents a natural, readerfriendly way to learn some of the essential ideas of graph theory starting from first principles. Most of these topics have been discussed in text books. 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. Yellen, graph theory and its applications, crc press, boca raton, 1999. A graph with such a labeling is an edge labeled graph. Nagarajan 2 investigate neighbourhood prime labeling for special graphs like friendship graph, gear, ladder, triangular book and.
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. 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. A difference labeling of g is an injection f from v to the set of non. The helm graph is a labeled graph with common weight decomposition. The notion of prime labeling was originated by entringer and was discussed in a. In this paper, we consider when ladder graphs are prime and when the corresponding labeling may be done in a cyclic manner around. On neighbourhood prime labeling of certain classes of graphs. Thus in all the possibilities f1 admits a prime labeling for 1. For all other terminology and notations we follows harary harary 1972. In this paper we investigate prime labeling for some helm related 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 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. Pdf a graph g v, e with n vertices is said to admit prime labeling if its vertices. Online shopping for graph theory from a great selection at books store.
The function defined above gives prime labeling for. 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. Moreover we prove that w n is a strongly prime graph for every even integer n. Graph theory has experienced a tremendous growth during the 20th century. 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. A prime labeling of a graph is an injective function f. A prime labeling of a graph of order is an injective function such that for every pair of adjacent vertices and.
The symbol vg and eg denotes the vertex set and edge set of a graph g. We investigate prime labeling for some graphs resulted by identifying any two vertices of some graphs. Square difference labeling, square difference graph. Covers basic graph theory and then goes off into a wide range of applications and analytic tools. 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.
We also introduce the concept of strongly prime graph and prove that the graphs cn, pn, and k1,n are strongly prime graphs. In this paper we prove that the split graphs of k1,n and bn,n are prime cordial graphs. A graph which satisfies the conditions of prime labeling and harmonious labeling is called a prime harmonious labeling. Acquaintanceship and friendship graphs describe whether people know each other. In this paper we investigate prime labeling for some fan related graphs. A graph which admits prime cordial labeling is called prime cordial graph. A graph g which admits prime labeling is called a prime graph. For the remainer of this paper whenever refering to a graph we will be refering to an edge labeled graph. Thus in each of the possibilities the graph g under consideration admits a prime labeling. Moreover we prove that wn is a strongly prime graph for every even integer n. For a simple graph g with n vertices in the vertex set vg, a prime labeling is an assignment of the. 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. Pdf some results on prime and kprime labeling researchgate.
It is known that cycles and bipartite graphs are prime distance graphs. Likewise, an edge labelling is a function of to a set of labels. Square difference prime labeling of some planar graphs. The graph admitting vertex prime labeling is called as verterx prime graph. In this paper we investigate prime labeling for k n e where e is an edge. Any graph produced in this way will have an important property. In the present work we investigate some classes of graphs which admit prime. Proof letg be a graph without cycles withn vertices and n. A second type, which might be called a triangular book, is the complete tripartite graph k 1,1,p. 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. It took a hundred years before the second important contribution of kirchhoff 9 had been made for the analysis of electrical networks. 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. Buy graph theory book online at low prices in india graph. A graph which admits a prime cordial labeling is called a prime cordial graph.
The square sum labeling and square sum graphs are 1 are defined and discussed by v. Nonplanar graphs can require more than four colors, for example this graph this is called the complete graph on ve vertices, denoted k5. Further we prove that the wheel graph wn admits prime cordial labeling for n. 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.
There are many kinds of graph labeling such as graceful labeling, magic labeling, prime labeling, and other different labeling techniques. In this paper we investigate some new families of vertex prime graphs. An outline of the results contained in all the chapters is given in the introduction. 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. They also show that a 2regular graph with at least two odd cycles has no vertex prime labeling.
The systematic study of number theory was initiated around 300b. E be a simple, undirected and nite graph with p vertices and q edges. Set theory, matrix maths and some calculus is a prerequisite to using the tools in this book. For graph theoretic terminology, we refer to harary 2. While most research has revolved around finding prime. If f is an injection from the vertices of g to the set 2,4,6. They proved that the cycle, complete graph kn, the cycle cactus, ladder and complete lattice grids are square. The format is similar to the companion text, combinatorics. Nagarajan 1 investigate neighbourhood prime labeling for some special graphs like friendship graph, gear, ladder, triangular book and coconut tree. Neighbourhood prime labeling on some graphs semantic scholar.
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