A note on automorphisms of halved Cayley graphs of Coxeter systems

We consider the halved Cayley graphs of Coxeter systems and show that every automorphism of such a graph can be uniquely extended to an automorphism of the corresponding Cayley graph. Obravnavamo razpolovljene Cayleyjeve grafe Coxeterjevih sistemov in pokažemo, da lahko vsak avtomorfizem takšnega grafa enolično razširimo do avtomorfizma ustreznega Cayleyjevega grafa.