Explorations in Algebraic Graph Theory with Sage

Chris Godsil

University of Waterloo
Department of Combinatorics and Optimization

Rob Beezer

University of Puget Sound
Department of Mathematics and Computer Science
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled “GNU Free Documentation License”.

Table of Contents

1. Getting Started
Getting Information
Fiddling with Vertices and Edges
2. First Projects
Pseudosimilar Vertices
Circle Graphs
Line Graphs and Covers
3. Cayley Graphs
Cayley Graphs
The Higman-Sims Graph
The 600-Cell
Cubelike Graphs
4. Distance-Regular Graphs
Distance Regularity
Generalized Quadrangles
The McLaughlin Graph
Drackns: Generating Parameter Sets
5. Polynomials and Power Series
Forbidden Words
Fractions and Series
Solving Equations
Counting Trees
6. Matrices
Continuous Quantum Walks
A. GNU Free Documentation License