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.