On distance two in Cayley graphs of Coxeter groups

Mark Pankov

On distance two in Cayley graphs of Coxeter groups

Combinatorics 2014-04-29 v2 Group Theory

Authors: Mark Pankov

Abstract

We consider the Cayley graph ${\rm C}(W,S)$ of a Coxeter system $(W,S)$ and describe all maximal $2$ -cliques in this graph, i.e. maximal subsets in the vertex set such that the distance between any two distinct elements is equal to $2$ . As an application, we show that every automorphism of the half of Cayley graph is uniquely extendable to an automorphism of the Cayley graph if $|S|\ge 5$ .

Keywords

Cayley graphs Coxeter groups distance two maximal 2-cliques automorphisms graph theory

Cite

@article{arxiv.1404.1479,
  title  = {On distance two in Cayley graphs of Coxeter groups},
  author = {Mark Pankov},
  journal= {arXiv preprint arXiv:1404.1479},
  year   = {2014}
}

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