图论教程

出版时间：2011-6  出版社：科学出版社  作者：（印）巴拉克里什南　等编著  页数：227  
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内容概要

Graph theory has experienced a
tremendous growth during the 20thcentury. One of the main reasons
for this phenomenon is theapplicability of graph theory in other
disciplines such as physics,chemistry, psychology, sociology, and
theoretical computer science.This book aims to provide a solid
background in the basic topics ofgraph theory. It covers Dirac's
theorem on k-connected graphs,Harary-Nashwilliam's theorem on the
hamiltonicity of line graphs,Toida-McKee's characterization of
Eulerian graphs, the Tutte matrixof a graph, Foumier's proof of
Kuratowski's theorem on planar graphs,the proof of the
nonhamiltonicity of the Tutte graph on 46 verticesand a concrete
application of triangulated graphs. The book does notpresuppose
deep knowledge of any'branch of mathematics, butrequires only the
basics of mathematics. It can be used in an advancedundergraduate
course ora beginning graduate course in graph theory.

作者简介

作者：（印度）巴拉克里什南（R.Balakrishnan） （印度）K.Ranganathan

书籍目录

Preface
Ⅰ  Basic Results
  1.0  Introduction
  1.1  Basic Concepts
  t.2  Subgraphs
  1.3  Degrees of Vertices
  1.4  Paths and Connectedness
  1.5  Automorphism of a Simple Graph
  1.6  Line Graphs
  1.7  Operations on Graphs
  1.8  An Application to Chemistry
  1.9  Miscellaneous Exercises
  Notes
Ⅱ  Directed Graphs
  2.0  Introduction
  2.1  Basic Concepts
  2.2  Tournaments
  2.3  k-Partite Tournaments
  Notes
Ⅲ  Connectivity
  3.0  Introduction
  3.1  Vertex Cuts and Edge Cuts
  3.2  Connectivity and Edge-Connectivity
  3.3  Blocks
  3.4  Cyclical Edge-Connectivity of a Graph
  3.5  Menger's Theorem
  3.6  Exercises
  Notes
Ⅳ  Trees
  4.0  Introduction
  4.1  Definition, Characterization, and Simple Properties
  4.2  Centers and Centroids
  4.3  Counting the Number of Spanning Trees
  4.4  Cayley's Formula
  4.5  Helly Property
  4.6  Exercises
  Notes
Ⅴ  Independent Sets and Matehings
  5.0  Introduction
  5.1  Vertex Independent Sets and Vertex Coverings
  5.2  Edge-Independent Sets
  5.3  Matchings and Factors
  5.4  Matchings in Bipartite Graphs
  5.5*  Perfect Matchings and the Tutte Matrix
  Notes
Ⅵ  Eulerian and Hamiltonian Graphs
  6.0  Introduction
  6.1  Eulerian Graphs
  6.2  Hamiltonian Graphs
  6.3*  Pancyclic Graphs
  6.4  Hamilton Cycles in Line Graphs
  6.5  2-Factorable Graphs
  6.6  Exercises
  Notes
Ⅶ  Graph Colorings
  7.0  Introduction
  7.1  Vertex Colorings
  7.2  Critical Graphs
  7.3  Triangle-Free Graphs
  7.4  Edge Colorings of Graphs
  7.5  Snarks
  7.6  Kirkman's Schoolgirls Problem
  7.7  Chromatic Polynomials
  Notes
Ⅷ Planarity
  8.0  Introduction
  8.1  Planar and Nonplanar Graphs
  8.2  Euler Formula and Its Consequences
  8.3  Ks and K3.3 are Nonplanar Graphs
  8.4  Dual of a Plane Graph
  8.5  The Four-Color Theorem and the Heawood Five-Color Theorem
  8.6  Kuratowski's Theorem
  8.7  Hamiltonian Plane Graphs
  8.8  Tait Coloring
  Notes
Ⅸ  Triangulated Graphs
  9.0  Introduction
  9.1  Perfect Graphs
  9.2  Triangulated Graphs
  9.3  Interval Graphs
  9.4  Bipartite Graph B（G） of a Graph G
  9.5  Circular Arc Graphs
  9.6  Exercises
  9.7  Phasing of Traffic Lights at a Road Junction
  Notes
Ⅹ  Applications
  10.0  Introduction
  10.1  The Connector Problem
  10.2  Kruskal's Algorithm
  10.3  Prim's Algorithm
  10.4  Shortest-Path Problems
  10.5  Timetable Problem
  10.6  Application to Social Psychology
  10.7  Exercises
  Notes
List of Symbols
References
Index

章节摘录

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用户评论 (总计1条)

•   内容很具体，有形象的解释和图~便于学习，很新喔，惹人爱喔