E book Particulars :
Language English
Pages 598
Format PDF
Dimension 31.1 MB

 

Graph Theory with Applications to Engineering and Computer Science


 

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

Contents of Graph Theory PDF


  • 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

Preface to Graph Theory PDF


The final 20 years have witnessed an upsurge of curiosity and exercise in graph principle, notably amongst utilized mathematicians and engineers.

Clear proof of that is to be present in an unprecedented progress within the variety of papers and books being revealed within the subject.

In 1957 there was precisely one ebook on the topic (particularly, König’s Théorie der Endlichen und Unendlichen Graphen).

Now, sixteen years later, there are over two dozen textbooks on graph principle, and virtually an equal variety of proceedings of varied seminars and conferences.

 

Every ebook has its personal power and factors of emphasis, relying on the axe (or the pen) the writer has to grind. I’ve emphasised the computational and algorithmic features of graphs.

This emphasis arises from the expertise and conviction that every time graph principle is utilized to fixing any sensible downside (be it in electrical community evaluation, in circuit format,

In knowledge constructions, in operations analysis, or in social sciences), it virtually all the time leads to massive graphs—graphs which might be nearly inconceivable to analyze with out assistance from the pc.

An engineer typically finds that these real-life issues that may be modeled into graphs sufficiently small to be labored on by hand are additionally sufficiently small to be solved by means apart from graph principle.

(On this respect graph principle is completely different from faculty algebra, elementary calculus, or complicated variables.)

The truth is, the high-speed digital laptop is likely one of the causes for the latest progress of curiosity in graph principle.

Satisfied {that a} scholar of utilized graph principle should be taught to enlist the assistance of a digital laptop for dealing with massive graphs, I’ve emphasised algorithms and their efficiencies.

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

Chapter 11, the most important within the ebook, is devoted completely to computational features of graph principle, together with graph-theoretic algorithms and samples of a number of examined laptop applications for fixing issues on graphs.

I imagine this strategy has not been utilized in any of the sooner books on graph principle. The fabric coated in Chapter 11 and in lots of sections from different chapters is showing for the primary time in any textbook.

But the utilized and algorithmic facet of this ebook has not been allowed to spoil the rigor and mathematical magnificence of graph principle.

Certainly, the ebook incorporates sufficient materials for a course in “pure” graph principle. The ebook has been made as a lot self-contained as was doable.

The extent of presentation is suitable for superior undergraduate and firstyear graduate college students in all disciplines requiring graph principle.

The ebook is organized in order that the primary half (Chapters 1 by way of 9) serves as important and introductory materials on graph principle.

This portion requires no particular background, besides some elementary ideas from set principle and matrix algebra and, in fact, a certain quantity of mathematical maturity.

Though the illustrations of purposes are interwoven with the speculation even on this portion, the examples chosen are brief and largely of the character of puzzles and video games.

That is completed so {that a} scholar in virtually any subject can learn and grasp the primary half.

The second half of the ebook is extra superior, and completely different chapters require completely different backgrounds as they deal with purposes to nontrivial, real-world, complicated issues in numerous fields.

Retaining this in thoughts, Chapters 10 by way of 15 have been made impartial of one another.

One may research a later chapter with out going by way of the sooner ones, offered the primary 9 chapters have been coated.

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