图与网络 2012-2013春季学期 2011级数学

任课老师

基本信息

学分:4.0

学时:68

时间:星期二14:00-15:40&星期五10:00-11:40

地点: 下院411

课程代码:MA336

教学大纲

  1. Definitions and Examples of Graphs and Digraphs
  2. Paths and Cycles: Connectivity of graphs, Eulerian and Hamiltonian graphs
  3. Trees: Fundamental properties of trees and spanning trees
  4. Cycles and Cuts
  5. Adjacency matrix of a graph and spectrum of a graph
  6. Laplacian of a graph
  7. Matrix-Tree Theorem
  8. Planarity of Graphs
  9. Coloring of Graphs
  10. Flows in Networks
  11. Matchings and Hall’s Marriage Theorem
  12. Network Flows and Mini-Max Theorem
  13. Menger’s Theorem
  14. Electric Networks
  15. Linear Algebraic Method to study Networks
  16. Integer Flows

参考教材

Introduction to Graph Theory (5th edition) by Robin Wilson