File : pdf, 23.4 MB, 270 pages
by J.A. Bondy and U.S.R. Murty
TOC
1. Graph and Subgraphs
1.1 Graphs and Simple Graphs
Graph Isomorphism
The Incidence and Adjacency Matrices
Subgraphs
Vertex Degrees
Paths and Connection
Cycles
Applications
The Shortest Path Problem
Sperner’s Lemma
2. Trees
Trees
Cut Edges and Bonds
Cut Vertices
Gayley’s Formula
The Connector Problem
3. Connectivity
Blocks
Construction of Reliable Communication Networks
4. Euler Tours and Hamilton Cycles
Euler Tours
Hamilton Cycles
The Chinese Postman Problem
The Travelling Salesman Problem
5. Matchings
Matchings
Matchings and Coverings in Bipartite Graphs
Perfect Matchings
The Personnel Assignment Problem
The Optimal Assignment Problem
6. Edge Colourings
Edge Chromatic Number
Vizing’s Theorem
The Timetabling Problem
7. Independent Sets and Cliques
Independent Sets
Ramsey’s Theorem
Turan’s Theorem
Schur’s Theorem
A Geometry Problem
8. Vertex Colourings
Chromatic Number
Brook’s Theorem
Hajo’s Conjecture
Chromatic Polynomials
Girth and Chromatic Number
A Storage Problem
9. Planar Graphs
Plane and Planar Graphs
Dual Graps
Euler’s Formula
Bridges
Kuratowski’s Theorem
The Five-Colour Theorem and Four-Coulour Conjecture
Nonhamiltonian Planar Graphs
A Planarity Algorithm
10. Directed Graphs
Directed Graphs
Directed Paths
Directed Cycles
A Job Sequencing Problem
Designing an Efficient Computer Drum
Making a Road System One-Way
Ranking the Participants in a Tournament
11. Networks
Flows
Cuts
The Maz-Flow Min-Cut Theorem
Menger’s Theorem
Feasible Flwols
12. The Cycle Space and Bond Space
Circulation and Potential Differences
The Number of Spanning Trees
Perfect Squares
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