The Excess Zero Graph of a Coxeter Group

Sarah Hart; Veronica Kelsey; Peter Rowley

The Excess Zero Graph of a Coxeter Group

Group Theory 2025-04-23 v1

Authors: Sarah Hart , Veronica Kelsey , Peter Rowley

Abstract

For a Coxeter group $W$ with length function $\ell$ , the excess zero graph $\mathcal{E}_0(W)$ has vertex set the non-identity involutions of $W$ , with two involutions $x$ and $y$ adjacent whenever $\ell(xy)=\ell(x)+\ell(y)$ . Properties of this graph such as connectivity, diameter and valencies of certain vertices of $\mathcal{E}_0(W)$ are explored.

Keywords

coxeter groups graph theory

Cite

@article{arxiv.2504.15994,
  title  = {The Excess Zero Graph of a Coxeter Group},
  author = {Sarah Hart and Veronica Kelsey and Peter Rowley},
  journal= {arXiv preprint arXiv:2504.15994},
  year   = {2025}
}

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