Commuting involution graphs in classical affine Weyl groups. Issue 7 (2nd July 2020) - Hart, Sarah; Sbeiti Clarke, Amal
Abstract: In this paper we investigate commuting involution graphs in classical affine Weyl groups. Let W be a classical Weyl group of rank n, with W ˜ its corresponding affine Weyl group. Our main result is that if X is a conjugacy class of involutions in W ˜, then the commuting involution graph C ( W ˜, X ) is either disconnected or has diameter at most n  + 2. This bound is known to hold for types A ˜ n and C ˜ n, so the main work of this paper is to prove the theorem for types B ˜ n and D ˜ n .