Free online book “Graph Theory with Applications” by J. A. Bondy and U. S. R. Murty. This book is intended as an introduction to graph theory. Our aim has been to present what we consider to be the basic material, together with a wide variety of applications, both to other branches of mathematics and to real-world problems. Included are simple new proofs of theorems of Brooks, Chvatal, Tutte and Vizing.

**Description**

The applications have been carefully selected, and are treated in some depth. We have chosen to omit all so-called “applications” that employ just the language of graphs and no theory. The applications appearing at the end of each chapter actually make use of theory developed earlier in the same chapter. We have also stressed the importance of efficient methods of solving problems. Several good algorithms are included and their efficiencies are analysed. We do not, however, go into the computer implementation of these algorithms.

**Contents**

- Graphs and Subgraphs
- Trees
- Connectivity
- Euler Tours and Hamilton Cycles
- Matchings
- Edge Colourings
- Independent Sets and Cliques
- Vertex Colourings
- Planar Graphs
- Directed Graphs
- Networks
- The Cycle Space and Bond Space

**Book Details**