Geodesic
Some remarks on symmetrical extensions of graphs
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 284-293 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that results from a previous paper of the author on symmetrical $2$-extensions of graphs can be extended to symmetrical $p$-extensions of graphs for any prime $p$. In particular, it is proved that for any prime $p$ there are only finitely many symmetrical $p$-extensions of a locally finite graph which has an abelian subgroup of finite index in its automorphism group. Some refinements of these results are also proved. In addition, it is considered a question on the possibility to represent symmetrical extensions of a $d$-dimension grid (and similar graphs) in the $d$-dimension affine Euclidean space in such a way that a corresponding vertex-transitive group of automorphisms of the extension is induced by some crystallographic group of the space.
Keywords: graph, group of automorphisms, symmetrical extension of graphs. 
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V. I. Trofimov. Some remarks on symmetrical extensions of graphs. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 284-293. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a24/

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