Mean labeling on degree splitting graph of star graph. The 7page book graph of this type provides an example of a graph with no harmonious labeling. Many problems are easy to state and have natural visual representations, inviting exploration by new students and professional mathematicians. This is an interesting area of graph theory as well as psychology to be studied that. Revathi department of mathematics seethalakshmi ramaswami college tiruchirappalli 620002. A graph g with p vertices and q edges is called a harmonic mean graph if it is possible to label the vertices x. A graph with a minimal number of edges which is connected. Graph is a mathematical representation of a network and it describes the relationship between lines and points. The labeled property graph is one of the most popular ways of modeling graph data.
A common theme in graph labeling papers is to build up graphs that have. Smarandachely kconstrained labelingsmarandachely super mmean graph, smarandachely uniform kgraph. In this thesis, we consider graph labelings that have weights associated with each edge. Vertex odd mean and even mean labeling of some graphs n. A graceful labeling in a graph with p verticespoints and q edgeslines is. Harmonic mean labeling for some special graphs sandhya. In a weighted graph, the weight of a path is the sum of the weights of the edges traversed. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. Nonplanar graphs can require more than four colors, for example this graph this is called the complete graph on ve vertices, denoted k5. Odd mean labeling of chain of graphs sciencedirect. Some of them will appeared in my books automorphism.
This concise, selfcontained exposition is unique in its focus on the theory. Hence g is a skolem odd difference mean labeling of g p n for all n p 2. One of the important areas in graph theory is graph labeling used in many applications like coding theory, xray crystallography, radar, astronomy. The field of graph theory plays vital role in various fields. Vertex odd mean and even mean labeling of some graphs. Most of these topics have been discussed in text books. We consider the mean labeling for degree splitting graph of single star and two star graphs. Graph theory by reinhard diestel, introductory graph theory by gary chartrand, handbook of graphs and networks. 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. Graph theory, branch of mathematics concerned with networks of points connected by lines. A graph with no cycle in which adding any edge creates a cycle.
What are some of the best books on graph theory, particularly directed towards an upper division undergraduate student who has taken most the standard undergraduate courses. A graph with n nodes and n1 edges that is connected. One vertex union of t isomorphic and non isomorphic cycles, cycle with pendent vertices, wheel graph when n is odd, are prime graphs. Barioli used it to mean a graph composed of a number of arbitrary subgraphs having two vertices in common. 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 path may be infinite, but a finite path always has a first vertex, called its start vertex, and a last vertex, called its end vertex. Read studies in graph theory magic labeling and related concepts book. Although in classic graph theory a label applies to a single node, its now commonly used to mean. Umbrella graph, p nqs n graph, c nq sn graphs are square difference graphs. Gallian, a dynamic survey of graph labeling, the electronic journal of combinatorics, 20. Hebbare 27 used the term bigraceful to mean a bipartite graceful graph.
A graph in which any two nodes are connected by a unique path path edges may only be traversed once. A graph labeling is an assignment of integers to the vertices or edges or both, subject to certain conditions and a detailed survey of graph labeling can be found in. We prove that splitting graph of the star graph and triangular book graph are 4cordial. Also, we say that a degree splitting graph for n star is a mean graph if n. Graph theorydefinitions wikibooks, open books for an. Diestel is excellent and has a free version available online. The book includes number of quasiindependent topics. Graph theory, narosa publishing house, new delhi, 1988. Some of the major themes in graph theory are shown in figure 3. Find the top 100 most popular items in amazon books best sellers.
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. A second type, which might be called a triangular book, is the complete tripartite graph k 1,1,p. The concepts of graph labeling began about 50 years ago, and have been research topics for many mathematicians all over the world. Studies in graph theory magic labeling and related. Mathematical combinatorics international book series, vol. A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. In graph theory, a path in a graph is a sequence of vertices such that from each of its vertices there is an edge to the next vertex in the sequence. What introductory book on graph theory would you recommend. A graph with maximal number of edges without a cycle. In this paper we find the radio mean number of graphs with diameter three, lotus inside a circle, helms and sunflower graphs. A function f is called an even mean labeling of a graph g with p vertices and q edges.
An enormous body of literature has grown around graph labeling. Mean labeling 110 let g be a graph obtained by arbitrary supersubdivision of path p n that is, for 1 i n 1 each edge e i of the path p n is replaced by a complete bipartite graph k 2. Pdf vertex odd mean and even mean labeling of some. A graph consists of some points and lines between them.
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. Being precise, we want to label vertices of a graph g with binary strings elements of the set 0, 1l. In this paper further result on odd mean labeling is discussed. Acharya 22 proved that every graph can be embedded as an induced subgraph of a graceful graph and a connected graph can be embedded as an induced subgraph of a graceful connected graph. An example usage of graph theory in other scientific. The geometric mean labelling of graphs have been defined in which the edge labels may be.
Make sure that you do not copy verbatim more than two words in a row from the text you have found. A difference labeling of g is an injection f from v to the set of non. I was thinking of any applications like scheduling etc. Results on vertex odd mean and even mean labeling theorem 2. The length of the lines and position of the points do not matter. On graph labeling, possibilities and role of mindconsciousness, graph theory advanced algorithms and applications, beril sirmacek. The goal of this textbook is to present the fundamentals of graph theory. Applications of graph labeling in communication networks. Graph labeling is one of the fascinating areas of graph theory with wide ranging applications.
Labeling, covering and decomposing of graphs citeseerx. Introduction all graphs in this paper are simple finite undirected and nontrivial graph gv, e with vertex set v and the edge set e. An example usage of graph theory in other scientific fields. Pdf we discuss here 4cordial labeling of three graphs.
Heron mean labeling of graphs international journal of. The subject of graph theory had its beginnings in recreational math problems see number game, but it has grown. A bijection mapping that assigns natural numbers to vertices andor edges of a graph is called a labeling. Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to practical problems. An illustrative introduction to graph theory and its applications graph theory can be difficult to understandgraph theory represents one of the most. Let v be vertex of k1 and v1, v2, vn be the vertices of the cycle. A graph g with p vertices and q edges is a mean graph. Square difference labeling, square difference graph. A graph in this context is made up of vertices also called nodes or. Graph theory is a fascinating and inviting branch of mathematics. If it observed that the blue circles are entitles nodesvertices and the black curves are entitled edges.
If you do use more than two words together, you will have to use quotation. Any graph produced in this way will have an important property. Buy studies in graph theory magic labeling and related concepts book online at best prices in india on. If the question related directly to the mathematical subject of graph theory, then consider the windmill graph. A path may be infinite, but a finite path always has. I would include in addition basic results in algebraic graph theory, say kirchhoffs theorem, i would expand the chapter on algorithms, but the book. Mean labeling of some graphs international journal of. A function f is called an even mean labeling of a graph g. A graph with a mean cordial labeling is called a mean cor dial graph. In this paper the centroidal mean labeling of cycle containing graphs such as triangular ladder t l n, cycle c n, polygonal chain g mn, square graph p 2 n, l n k 1,2, ladder l n are found. Normal perception has a private and illogical meaning. What are some good books for selfstudying graph theory.