A Note on Commuting Involution Graphs in Affine Coxeter Groups

Abstract

Commuting involution graphs have been studied for finite Coxeter groups and for affine groups of classical type. The purpose of this short note is to establish some general results for commuting involution graphs in affine Coxeter groups, and to deal with types $\tilde F_4$ and $\tilde G_2$. Types $\tilde E_6$ $\tilde E_7$ and $\tilde E_8$ are more substantial and we will address these in a forthcoming paper.