The Excess Zero Graph of a Coxeter Group

2025/04/22 by Hart, Sarah, Kelsey, Veronica, Rowley, Peter
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2504.15994

Abstract

For a Coxeter group W with length function ℓ, the excess zero graph E₀(W) has vertex set the non-identity involutions of W, with two involutions x and y adjacent whenever ℓ(xy)=ℓ(x)+ℓ(y). Properties of this graph such as connectivity, diameter and valencies of certain vertices of E₀(W) are explored.

Related

• Maximal length elements of excess zero in finite Coxeter groups
• On Excess in Finite Coxeter Groups
• Involutions in Coxeter groups
• Classification of Coxeter groups with finitely many elements of a-value 2
• A Note on Commuting Involution Graphs in Affine Coxeter Groups