This is an outline for a short course on generalized quadrangles. The secret aim is to provide an introduction to many interesting topics from algebraic graph theory. The explicit aim is to provide a counter-example to a proposed algorithm for testing isomorphism of strongly regular graphs.
Actual Topics
- Axioms and incidence structures. Examples: $L(K_{m,n}$, edges and 1-factors of $K_6$) Incidence graphs, bipartite graphs with diameter 4 and girth 8. Duality.
- Degenerate cases. Thick GQs are semiregular.
- Symplectic GQs. Are they self-dual?
- Point and line graphs of thick GQs are strongly regular. What does this mean?
- SRGS: parameters, eigenvalues, spectral decomposition.
- $s\le t^2$, Krein bounds.
- known families of GQs, unitary GQs.
- ovoids and spreads, covers.
- flock GQs.