Geodesic
Trees and reflection groups.
The electronic journal of combinatorics, Tome 12 (2005)

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Zbl EuDML
We define a reflection in a tree as an involutive automorphism whose set of fixed points is a geodesic and prove that, for the case of a homogeneous tree of degree $4k$, the topological closure of the group generated by reflections has index $2$ in the group of automorphisms of the tree.
DOI : 10.37236/1912
Classification : 20E08, 05C05, 05C25
Mots-clés : reflections in trees, involutive automorphisms, homogeneous trees, groups of automorphisms, groups generated by reflections 
Humberto Luiz Talpo; Marcelo Firer. Trees and reflection groups.. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1912
@article{10_37236_1912,
     author = {Humberto Luiz Talpo and Marcelo Firer},
     title = {Trees and reflection groups.},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1912},
     zbl = {1110.20021},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1912/}
}
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