A path may be infinite, but a finite path always has. The subject of graph theory had its beginnings in recreational math problems see number game, but it has grown. A graph in this context is made up of vertices also called nodes or. 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. Mean labeling on degree splitting graph of star graph. An illustrative introduction to graph theory and its applications graph theory can be difficult to understandgraph theory represents one of the most. Hebbare 27 used the term bigraceful to mean a bipartite graceful graph. A function f is called an even mean labeling of a graph g. 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. Results on vertex odd mean and even mean labeling theorem 2. A graph consists of some points and lines between them. In this paper we find the radio mean number of graphs with diameter three, lotus inside a circle, helms and sunflower graphs.
Mathematical combinatorics international book series, vol. 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. Graph labeling is one of the fascinating areas of graph theory with wide ranging applications. The goal of this textbook is to present the fundamentals of graph theory. A graph g with p vertices and q edges is called a harmonic mean graph if it is possible to label the vertices x. Graph theorydefinitions wikibooks, open books for an. A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to practical problems. The condition for a graph to be odd mean is that p.
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 difference labeling of g is an injection f from v to the set of non. 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. The book includes number of quasiindependent topics. An enormous body of literature has grown around graph labeling. A graceful labeling in a graph with p verticespoints and q edgeslines is. The geometric mean labelling of graphs have been defined in which the edge labels may be. Any graph produced in this way will have an important property. Studies in graph theory magic labeling and related. Find the top 100 most popular items in amazon books best sellers. Graph theory by reinhard diestel, introductory graph theory by gary chartrand, handbook of graphs and networks. 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. One of the important areas in graph theory is graph labeling used in many applications like coding theory, xray crystallography, radar, astronomy.
Revathi department of mathematics seethalakshmi ramaswami college tiruchirappalli 620002. Being precise, we want to label vertices of a graph g with binary strings elements of the set 0, 1l. An example usage of graph theory in other scientific fields. Read studies in graph theory magic labeling and related concepts book. Some of them will appeared in my books automorphism. Vertex odd mean and even mean labeling of some graphs. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. Pdf we discuss here 4cordial labeling of three graphs.
The length of the lines and position of the points do not matter. Also, we say that a degree splitting graph for n star is a mean graph if n. Barioli used it to mean a graph composed of a number of arbitrary subgraphs having two vertices in common. We consider the mean labeling for degree splitting graph of single star and two star graphs. A graph with no cycle in which adding any edge creates a cycle. Normal perception has a private and illogical meaning. On graph labeling, possibilities and role of mindconsciousness, graph theory advanced algorithms and applications, beril sirmacek. A graph with a mean cordial labeling is called a mean cor dial graph. A bijection mapping that assigns natural numbers to vertices andor edges of a graph is called a labeling. Graph theory is a fascinating and inviting branch of mathematics. Graph theory, narosa publishing house, new delhi, 1988. This concise, selfcontained exposition is unique in its focus on the theory. Applications of graph labeling in communication networks.
If you do use more than two words together, you will have to use quotation. A second type, which might be called a triangular book, is the complete tripartite graph k 1,1,p. 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. Gallian, a dynamic survey of graph labeling, the electronic journal of combinatorics, 20. Diestel is excellent and has a free version available online. Labeling, covering and decomposing of graphs citeseerx. Heron mean labeling of graphs international journal of. If the question related directly to the mathematical subject of graph theory, then consider the windmill graph. I was thinking of any applications like scheduling etc. Mean labeling of some graphs international journal of. Many problems are easy to state and have natural visual representations, inviting exploration by new students and professional mathematicians. Most of these topics have been discussed in text books. 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. 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.
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. Buy studies in graph theory magic labeling and related concepts book online at best prices in india on. Square difference labeling, square difference graph. In a weighted graph, the weight of a path is the sum of the weights of the edges traversed. Make sure that you do not copy verbatim more than two words in a row from the text you have found. A graph in which any two nodes are connected by a unique path path edges may only be traversed once. In this thesis, we consider graph labelings that have weights associated with each edge.
A common theme in graph labeling papers is to build up graphs that have. The field of graph theory plays vital role in various fields. A graph with maximal number of edges without a cycle. A graph with a minimal number of edges which is connected. Although in classic graph theory a label applies to a single node, its now commonly used to mean. Harmonic mean labeling for some special graphs sandhya.
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. What are some good books for selfstudying graph theory. A graph with n nodes and n1 edges that is connected. Graph theory, branch of mathematics concerned with networks of points connected by lines. Let v be vertex of k1 and v1, v2, vn be the vertices of the cycle. A function f is called an even mean labeling of a graph g with p vertices and q edges.
Graph is a mathematical representation of a network and it describes the relationship between lines and points. Vertex odd mean and even mean labeling of some graphs n. Pdf vertex odd mean and even mean labeling of some. 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. Nonplanar graphs can require more than four colors, for example this graph this is called the complete graph on ve vertices, denoted k5. What introductory book on graph theory would you recommend. I would include in addition basic results in algebraic graph theory, say kirchhoffs theorem, i would expand the chapter on algorithms, but the book. Buy studies in graph theory magic labeling and related. This is an interesting area of graph theory as well as psychology to be studied that. Odd mean labeling of chain of graphs sciencedirect.
If it observed that the blue circles are entitles nodesvertices and the black curves are entitled edges. Some of the major themes in graph theory are shown in figure 3. Hence g is a skolem odd difference mean labeling of g p n for all n p 2. It is not the easiest book around, but it runs deep and has a nice unifying theme of studying how.
584 1572 1054 1158 726 1191 1596 270 1251 1128 1482 773 134 1528 505 587 933 916 629 1300 1199 275 459 1088 1132 529 484 39 3 92 894 843 896 92 769