Graphs of Coxeter and Lie Type

In this chapter we study Coxeter systems and Tits systems and certain graphs derived from these. In the first few sections finiteness is not assumed. In the later sections almost all known infinite families of distance-transitive graphs are described in this framework. The chapter ends with a determination of all distance-transitive graphs which naturally arise from a Tits system in a finite Chevalley group. Much more information on Tits systems, Chevalley groups and buildings can be found in Bourbaki [113], Carter [187, 188] and Tits [747, 753].