The finiteness of the number of symmetrical 2-extensions of the $d$-dimensional lattice and similar graphs
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 290-303
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We prove that there are only finitely many symmetrical $2$-extensions of a locally finite graph whenever the automorphism group of the graph has an abelian subgroup of finite index (this case is of interest for certain applications). Some refinements and generalizations of this result are also given.
Keywords:
graph, group of automorphisms, symmetrical extension of graphs.
@article{TIMM_2013_19_3_a30,
author = {V. I. Trofimov},
title = {The finiteness of the number of symmetrical 2-extensions of the $d$-dimensional lattice and similar graphs},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {290--303},
publisher = {mathdoc},
volume = {19},
number = {3},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a30/}
}
TY - JOUR AU - V. I. Trofimov TI - The finiteness of the number of symmetrical 2-extensions of the $d$-dimensional lattice and similar graphs JO - Trudy Instituta matematiki i mehaniki PY - 2013 SP - 290 EP - 303 VL - 19 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a30/ LA - ru ID - TIMM_2013_19_3_a30 ER -
%0 Journal Article %A V. I. Trofimov %T The finiteness of the number of symmetrical 2-extensions of the $d$-dimensional lattice and similar graphs %J Trudy Instituta matematiki i mehaniki %D 2013 %P 290-303 %V 19 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a30/ %G ru %F TIMM_2013_19_3_a30
V. I. Trofimov. The finiteness of the number of symmetrical 2-extensions of the $d$-dimensional lattice and similar graphs. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 290-303. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a30/