Algebraic graph theory is a combination of two strands. The first is the study of algebraic objects associated with graphs. The second is the use of tools from algebra to derive properties of graphs. The authors's goal has been to present and illustrate the main tools and ideas of algebraic graph theory, with an emphasis on current rather then classical topics. While placing a strong emphasis on concrete examples they tried to keep the treatment self-contained.

1 Graphs

2 Groups

3 Transitive Graphs

4 Arc-Transitive Graphs

5 Generalized Polygons and Moore Graphs

6 Homomorphisms

7 Kneser Graphs

8 Matrix Theory

9 Inter lacing

10 Strongly Regular Graphs

11 Two-Graphs

12 Line Graphs and Eigenvalues

13 The Laplacian of a Graph

14 Cuts and Flows

15 The Rank Polynomial

16 Knots

17 Knots and Eulerian Cycles

Review

C. Godsil and G.F. Royle

Algebraic Graph Theory

"A welcome addition to the literature . . . beautifully written and wide-ranging in its coverage."―MATHEMATICAL REVIEWS

"An accessible introduction to the research literature and to important open questions in modern algebraic graph theory"―L'ENSEIGNEMENT MATHEMATIQUE