Geodesic
The finiteness of the number of symmetrical extensions of a locally finite tree by a finite graph
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 303-308

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We prove that there are only finitely many symmetrical extensions of a locally finite tree by a finite graph. Moreover, we prove that there are only finitely many pairwise nonequivalent realizations of symmetrical extensions of a locally finite tree by a finite graph.
Keywords: tree, symmetrical extension by a finite graph. 
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     author = {V. I. Trofimov},
     title = {The finiteness of the number of symmetrical extensions of a locally finite tree by a finite graph},
     journal = {Trudy Instituta matematiki i mehaniki},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a29/}
}
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V. I. Trofimov. The finiteness of the number of symmetrical extensions of a locally finite tree by a finite graph. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 303-308. http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a29/