Hardbound. Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals version continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails. The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. These have lead to new families of perfect graphs and many algorithmic results. A new Epilogue chapter in this second edition surveys many of the recent results in the area. It also gives pointers for further study. The book has served to unify the topic and to act as a sp
It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics.Key features:- Self-contained exposition of the theory of submodular functions.- Selected up-to-date materials substantial to future developments.- Polyhedral description of Discrete Convex Analysis.- Full description of submodular function minimization algorithms.- Effective insertion of figures.- Useful in applied mathematics, operations research, computer science, and economics.- Self-contained exposition of the theory of submodular functions.- Selected up-to-date materials substantial to future developments.- Polyhedral description of Discrete Convex Analysis.- Full description of submodular function minimization algorithms.- Effective insertion of figures.- Useful in applied mathematics, operations research, computer science, and economics.
Graph theory as a part of Discrete Mathematics has lots of application in the real world. This Book as an good introduction to graph theory will be a handy manual for all those who need a background of graph theory with all relevant definitions and examples. Basic results and theorems related to labeling are given with proof and examples. Some of the open problems are also posed. In Short, this will be a good starter pack for the graceful and harmonious labeling of graphs.
We want to show that this book is very important for the specialists in graph decomposition specially who work with orthogonal double cover for regular graphs, cayley graphs and circulant graphs and the persons who concerned with discrete mathematics and this book benefits the persons who worked with data bases and network analysis and we hope for all the readers for this book to get a good information after reading it.
The book presents some of the very fundamental ideas of spectral graph theory in a lucid way. The prerequisite is basic knowledge of graph theory and matrix algebra. It is intended to serve as a basic guide for the beginners in the field. Seeing to the vast area of applications, almost everybody has started appreciating graph theory as a very important branch of mathematics. Earlier, graph theory was isolated from other branches of mathematics. But combination of algebra and graph theory has started making wonders among mathematical community. We aspect that readers will surely find the book helpful to them.
Graph labeling has wide applications in the modelling and problems comes under the areas like Radar,Communication networks,Circuit design, Coding theory, Astronomy,Xray, DatabaseManagement, Crystallography and Modelling of Constraint Programming over Finite domain.So study on strong edges of labeled graphs has more importance.In this thesis I invented Strong Graphs,Properties of Strong ? labeled Graphs,A family of Strong Graphs,Nishad Graph,Properties of Nishad Graph,Nishad’s Algorithm,Properties of Nishad’s Algorithm, Application of Nishad Graph,Strength of a labeled Graph,Weak Graphs and weakness of a labeled graph,A family of weak graph and Nishad’s Method to find the strength and weakness of labeled Graphs.
Graph labeling is one of the fascinating areas of graph theory with wide ranging applications. Graph labelings were first introduced in the 1960’s where the vertices and edges are assigned real values or subsets of a set subject to certain conditions. An enormous body of literature has grown around graph labeling in the last five decades. Labeled graphs provide mathematical models for a broad range of applications. The qualitative labelings of a graph element have been used in diverse fields such as Conflict resolutions in Social psychology, Energy crises etc. Quantitative labelings of graph elements have been used in Missile guidance codes, Radar location codes, Coding theory, X-Ray Crystallography, Radio-Astronomy, Circuit design, Communication Network and the like Most popular graph labelings trace their origin to one introduced by Rosa This thesis is devoted to the study of magic strength of several graphs, super edge-magic labeling, and super edge-magic strength of several graphs, super vertex-magic labeling, total super magic labeling and anti super edge-magic labeling and the corresponding strengths.
This book caters to the needs of the students of various disciplines of both undergraduate and postgraduate courses, through effective formulation of graphical illustrations of quadratic residue cayley graphs. This comprehensive text introduces readers to the theory of dominating functions of quadratic residue cayley graphs. The neat free-body diagrams are presented and examples are solved systematically to make the procedure clear. Each of five chapters includes thorough grounding in the related concepts. In addition, the results and discussions designed to aid further understanding of the subject.
Most graph labeling methods trace their origin to one introduced by Alex Rosa, through the paper "On certain valuations of the vertices of a graph", which was presented in the International Symposium, held in Rome, July 1966,Gordon and Breach, N.Y. and Dunod Paris (1967) 349-355, or one given by R.L.Graham and N.J.A. Sloane, through the paper "On additive bases and harmonious graphs", SIAM J. Alg. Discrete Meth., 1 (1980) 382-404. Labeled graphs became a very useful tool for treating many problems in different branches of science, e.g. Electrical Networks, Coding Theory, Astronomy, X-Ray Crystallographic analysis. S. M. Hegde and S. Shetty defined what is called "Permutation and Combination Labelings". This book consists of some papers which give some rich additions to these two types of labelings.
This book is helpful to both undergraduate and postgraduate students through effective formulation of graphical illustrations of Divisor Cayley Graphs. It develops a thorough understanding of the structure of these graphs. Dominating Functions is one of the interesting topic of Graph Theory. In this text theory of dominating functions in Divisor Cayley Graphs is introduced. Also the concept of convex combination of dominating functions with explanation and neat free-body diagrams are presented. Some particular cases have been mentioned in the book and at the end a number of references have been included. In addition, the results and discussions designed to aid further understanding of the subject.This book will also be beneficial for researchers and useful for beginners who want to do research in these topics.
Szemeredi's Regularity Lemma is a powerful tool in Graph Theory, yielding many applications in areas such as Extremal Graph Theory, Combinatorial Number Theory and Theoretical Computer Science. Strong hypergraph extensions of graph regularity techniques were recently given by Nagle, Rodl, Schacht and Skokan, by W.T. Gowers, and subsequently, by T. Tao. These extensions have yielded quite a few non-trivial applications to Extremal Hypergraph Theory, Combinatorial Number Theory and Theoretical Computer Science. A main drawback to the hypergraph regularity techniques above is that they are highly technical. In this thesis, we consider a less technical version of hypergraph regularity which more directly generalizes Szemeredi's regularity lemma for graphs. The tools we discuss won't yield all applications of their stronger relatives, but yield still several applications in extremal hypergraph theory (for so-called linear or simple hypergraphs), including algorithmic ones. This thesis surveys these lighter regularity techiques, and develops three applications of them.
In this book 50 metrics in weighted graph and 53 metrics in fuzzy graph are introduced.Using 3 metrics the geodesics, convex hull,etc are introduced.The researchers can use these metrics to develop self centred fuzzy graphs and weighted graphs to simulate the transportation problems and communication networks.This book will be very useful to the researchers in graph theory, fuzzy mathematics ,and communication networks.
Matrix theory is a fundamental area of mathematics with applications not only to many branches of mathematics but also to science and engineering. It is a connection to many di?erent branches of mathematics such as Algebraic structures, Statistics, Combinatorics, including graphs and other discrete structures and Analysis, including systems of linear di?erential equations, function analysis and special functions.
Graph theory, as modern and young branches of mathematics, studies graphs which are abstract mathematical objects. The use of graph models for description or data structures is very common. Investigation of algorithms to solve problems using graph, is a very important part of computer science. The genetic algorithms represent a family of algorithms using some of genetic principles being present in nature, in order to solve particular computational problems. These natural principles are: inheritance, crossover, mutation, survival of the fittest, migrations and so on. The problems degree-limited graph of nodes considering the weight of the vertex or weight of the edges, with the aim to find the optimal weighted graph in terms of certain restrictions on the degree of the vertices in the subgraph. This class of combinatorial problems was extensively studied because of the implementation and application in network design, connection of networks and routing algorithms. It is likely that solution of MDBCS problem will find its place and application in these areas.
Flows in graphs present an important topic in modern mathematics with many applications in practice and a significant impact on many problems from discrete mathematics. Nowhere-zero flow in graphs present a dual concept for graph coloring problems. We apply methods of linear algebra for nowhere-zero flow problems. We present several results regarding the 5-flow conjecture. In particular, we give restrictions regarding cyclical edge connectivity and girth for a smallest counterexample to the conjecture. We present also application for edge-coloring of planar cubic graphs. Furthermore we present a decomposition formula for flow polynomials on graphs. The book is devoted for graduate students and researchers dealing with combinatorics.