• 1. Squaring the square ; 2. Knights errant ; 3. Graphs within graphs ; 4. Unsymmetrical electricity ; 5. Algebra in graph theory ; 6. Symmetry in graphs ; 7. Graphs on spheres ; 8. The cats of Cheshire ; 9. Reconstruction ; 10. Planar enumeration ; 11. The chromatic eigenvalues ; 12. In conclusion ; References ; Index

The book is not intended as a comprehensive treatise, and is not a textbook in the classical sense. It provides a unique and unusual introduction to graph theory by one of the founding fathers of the subject. The opening chapter tells of the first problems worked on by the author and his colleagues (collectively know as the Trintity Four). Their interests in graph theory was aroused by a problem in a mathematical puzzle book. Beginning with an account of their work on the construction of perfect squares and rectangles, the subsequent chapters describe the developement of the author's ideas: the disproof of Tait's conjecture on Hamiltonian circuits, factorizing graphs, algebra in graph theory, symmetry in graphs, graphs on spheres, and chromatic eigenvalues.