Graph Theory: Modeling, Applications, and Algorithms (美國原版) (圖論：建模、應用與演算法)

Description

For junior- to senior-level courses in Graph Theory taken by majors in Mathematics, Computer Science, or Engineering or for beginning-level graduate courses.

 

Once considered an “unimportant” branch of topology, graph theory has come into its own through many important contributions to a wide range of fields — and is now one of the fastest-growing areas in discrete mathematics and computer science. This new text introduces basic concepts, definitions, theorems, and examples from graph theory. The authors present a collection of interesting results from mathematics that involve key concepts and proof techniques; cover design and analysis of computer algorithms for solving problems in graph theory; and discuss applications of graph theory to the sciences. It is mathematically rigorous, but also practical, intuitive, and algorithmic.

 

 

 

Table of Contents

Preface                                                                                                     

1     Introduction to Graph Theory                                               

2     Basic Concepts in Graph Theory                                      

3     TreesandForests

4     Spanning Trees

5     Fundamental Properties of Graphs and Digraphs

6     Connectivity and Flow

7     Planar Graphs

8     Graph Coloring

9     Coloring Enumerations and Chordal Graphs

10    Independence,Dominance, and Matchings  

11    Cover Parameters and MatchingPolynomials

12    GraphCounting

13    Graph Algorithms

 

APPENDICES

A Greek Alphabet

B Notation

C Top Ten Online References

Index ix