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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2019, Volume 25, Number 4, Pages 226–234
DOI: https://doi.org/10.21538/0134-4889-2019-25-4-226-234 (Mi timm1688) 		 
On Limits of Vertex-Symmetric Graphs and Their Automorphisms

V. I. Trofimovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.21538/0134-4889-2019-25-4-226-234
Abstract: Using a simple but rather general method of constructing Cayley graphs with trivial vertex stabilizers, we give an example of an infinite locally finite Cayley graph (and, hence, an example of an infinite connected locally finite vertex-symmetric unimodular graph) which is isolated in the space of connected locally finite vertex-symmetric graphs. We also give examples of Cayley graphs which are not isolated in this space but are isolated from the set of connected vertex-symmetric finite graphs.
Keywords: connected locally finite vertex-symmetric graph, Cayley graph, convergence of graphs.
Received: 19.09.2019
Revised: 15.10.2019
Accepted: 21.10.2019
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2020, Volume 309, Issue 1, Pages S167–S174
DOI: https://doi.org/10.1134/S0081543820040185
Bibliographic databases:
Document Type: Article
UDC: 512.54+519.175
MSC: 05C25, 20F65, 20F69
Language: Russian
Citation: V. I. Trofimov, “On Limits of Vertex-Symmetric Graphs and Their Automorphisms”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 4, 2019, 226–234; Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S167–S174
Citation in format AMSBIB
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\paper On Limits of Vertex-Symmetric Graphs and Their Automorphisms
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\yr 2019
\vol 25
\issue 4
\pages 226--234
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2020
\vol 309
\issue , suppl. 1
\pages S167--S174
\crossref{https://doi.org/10.1134/S0081543820040185}
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