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Some remarks on symmetrical extensions of graphs

Content Provider	Springer Nature Link
Author	Trofimov, V. I.
Copyright Year	2015
Abstract	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 with an abelian subgroup of finite index in its automorphism group. Some refinements of these results are also obtained. In addition, we consider the question on the possibility to represent symmetrical extensions of a d-dimensional grid (and similar graphs) in the d-dimensional 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 motions of the space.
Starting Page	199
Ending Page	208
Page Count	10
File Format	PDF
ISSN	00815438
Journal	Proceedings of the Steklov Institute of Mathematics
Volume Number	289
Issue Number	1
e-ISSN	15318605
Language	English
Publisher	Pleiades Publishing
Publisher Date	2015-06-26
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	graph automorphism group symmetrical extension of graphs Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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