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Introduction to Graph Theory
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Authors: Vitaly I. Voloshin (Dept. of Mathematics, Physics and Computer Science, Troy Univ., Troy AL) 
Book Description:
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Graph Theory is an important area of contemporary mathematics with many applications in computer science, genetics, chemistry, engineering, industry, business and in social sciences. It is a young science invented and developing for solving challenging problems of ”computerized” society for which traditional areas of mathematics such as algebra or calculus are powerless.
This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking the courses in graph theory, discrete mathematics, data structures, algorithms. It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant
mathematics is required. The very basic facts from set theory, proof
techniques and algorithms are sufficient to understand it; but even those are explained in the text.
The book discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph coloring. The reader is conducted from the simplest examples, definitions and concepts, step by step, towards an understanding of a few most fundamental facts in the field.

The book may be used on undergraduate level for one semester introductory course. It includes many examples, figures and algorithms; each section ends with a set of exercises and a set of computer projects. The answers and hints to
selected exercises are provided at the end of the book. The material has been tested in class during more than 20-years of teaching experience of the author.

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Table of Contents:
Preface

1. Basic Definitions and Concepts, pp. 1-34
1.1 Fundamentals
1.2 Graph modeling applications
1.3 Graph representations
1.4 Generalizations
1.5 Basic graph classes
1.6 Basic graph operations
1.7 Basic subgraphs
1.8 Separation and connectivity

2. Trees and Bipartite Graphs, pp. 35-46
2.1 Trees and cyclomatic number
2.2 Trees and distance
2.3 Minimum spanning tree
2.4 Bipartite graphs

3. Chordal Graphs, pp. 47-62
3.1 Preliminary
3.2 Separators and simplicial vertices
3.3 Degrees
3.4 Distances in chordal graphs
3.5 Quasi-triangulated graphs

4. Planar Graphs, pp. 63-74
4.1 Plane and planar graphs
4.2 Euler’s formula
4.3 K5 and K3 3 are not planar graphs
4.4 Kuratowski’s theorem and planarity testing
4.5 Plane triangulations and dual graphs

5. Graph Coloring, pp. 75-118
5.1 Preliminary
5.2 Definitions and examples
5.3 Structure of colorings
5.4 Chromatic polynomial
5.5 Coloring chordal graphs
5.6 Coloring planar graphs
5.7 Perfect graphs
5.8 Edge coloring and Vizing’s theorem
5.9 Upper chromatic index

6. Graph Traversals and Flows, pp. 119-128
6.1 Eulerian graphs
6.2 Hamiltonian graphs
6.3 Network flows

7. Appendix, pp. 129-138
7.1 What is mathematical induction
7.2 Graph theory algorithms and their complexity
7.3 Answers and hints to selected exercises
7.4 Glossary of additional concepts

References pp.139-130

Index, pp. 141-144

   Binding: Hardcover
   Pub. Date: 2009, 1st quarter
   Pages: 144 pp.
   ISBN: 978-1-60692-374-0
   Status: AV
  
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
  
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Introduction to Graph Theory