Geodesic
Isomorphisms of Cayley graphs of surface groups
Algebra and discrete mathematics, no. 1 (2006), pp. 18-37.

Voir la notice de l'article provenant de la source Math-Net.Ru

A combinatorial proof is given for the fact that the Cayley graph of the fundamental group $\Gamma_g$ of the closed, orientable surface of genus $g\ge 2$ with respect to the usual generating set is isomorphic to the Cayley graph of a certain Coxeter group generated by $4g$ elements.
Keywords: Cayley graph
Mots-clés : Coxeter group. 
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Marek Bożejko; Ken Dykema; Franz Lehner. Isomorphisms of Cayley graphs of surface groups. Algebra and discrete mathematics, no. 1 (2006), pp. 18-37. http://geodesic.mathdoc.fr/item/ADM_2006_1_a1/