Graph Theory with Applications to Engineering and Computer Science

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Graph Theory with Applications to Engineering and Computer Science

PDF Free Download|Graph Theory with Applications to Engineering and Computer Science by Narsingh Deo .

Preface to Graph Theory PDF Book

The last two decades have witnessed an upsurge of interest and activity in graph theory, particularly among applied mathematicians and engineers.

Clear evidence of this is to be found in an unprecedented growth in the number of papers and books being published in the field.

In 1957 there was exactly one book on the subject (namely, König’s Théorie der Endlichen und Unendlichen Graphen).

Now, sixteen years later, there are over two dozen textbooks on graph theory, and almost an equal number of proceedings of various seminars and conferences.

Each book has its own strength and points of emphasis, depending on the axe (or the pen) the author has to grind. I have emphasized the computational and algorithmic aspects of graphs.

This emphasis arises from the experience and conviction that whenever graph theory is applied to solving any practical problem (be it in electrical network analysis, in circuit layout,

In data structures, in operations research, or in social sciences), it almost always leads to large graphs—graphs that are virtually impossible to analyze without the aid of the computer.

An engineer often finds that those real-life problems that can be modeled into graphs small enough to be worked on by hand are also small enough to be solved by means other than graph theory.

(In this respect graph theory is different from college algebra, elementary calculus, or complex variables.)

In fact, the high-speed digital computer is one of the reasons for the recent growth of interest in graph theory.

Convinced that a student of applied graph theory must learn to enlist the help of a digital computer for handling large graphs, I have emphasized algorithms and their efficiencies.

In proving theorems, constructive proofs have been given preference over nonconstructive existence proofs.

Chapter 11, the largest in the book, is devoted entirely to computational aspects of graph theory, including graph-theoretic algorithms and samples of several tested computer programs for solving problems on graphs.

I believe this approach has not been used in any of the earlier books on graph theory. The material covered in Chapter 11 and in many sections from other chapters is appearing for the first time in any textbook.

Yet the applied and algorithmic aspect of this book has not been allowed to spoil the rigor and mathematical elegance of graph theory.

Indeed, the book contains enough material for a course in “pure” graph theory. The book has been made as much self-contained as was possible.

The level of presentation is appropriate for advanced undergraduate and firstyear graduate students in all disciplines requiring graph theory.

The book is organized so that the first half (Chapters 1 through 9) serves as essential and introductory material on graph theory.

This portion requires no special background, except some elementary concepts from set theory and matrix algebra and, of course, a certain amount of mathematical maturity.

Although the illustrations of applications are interwoven with the theory even in this portion, the examples selected are short and mostly of the nature of puzzles and games.

This is done so that a student in almost any field can read and grasp the first half.

The second half of the book is more advanced, and different chapters require different backgrounds as they deal with applications to nontrivial, real-world, complex problems in different fields.

Keeping this in mind, Chapters 10 through 15 have been made independent of each other.

One could study a later chapter without going through the earlier ones, provided the first nine chapters have been covered.

Contents of Graph Theory PDF Book

  • INTRODUCTION
  • PATHS AND CIRCUITS
  • TREES AND FUNDAMENTAL CIRCUITS
  • CUT-SETS AND CUT-VERTICES
  • PLANAR AND DUAL GRAPHS
  • VECTOR SPACES OF A GRAPH
  • MATRIX REPRESENTATION OF GRAPHS
  • COLORING, COVERING, AND PARTITIONING
  • DIRECTED GRAPHS
  • ENUMERATION OF GRAPHS
  • GRAPH THEORETIC ALGORITHMS AND COMPUTER PROGRAMS
  • GRAPHS IN SWITCHING AND CODING THEORY
  • ELECTRICAL NETWORK ANALYSIS BY GRAPH THEORY
  • GRAPH THEORY IN OPERATIONS RESEARCH
  • SURVEY OF OTHER APPLICATIONS

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