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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 3, Pages 290–303 (Mi timm988)  
This article is cited in 5 scientific papers (total in 5 papers)

The finiteness of the number of symmetrical 2-extensions of the dd-dimensional lattice and similar graphs

V. I. Trofimovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University named after the First President of Russia B. N. Yeltsin
Full-text PDF (217 kB) Citations (5)
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Abstract: We prove that there are only finitely many symmetrical 22-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.
Received: 20.07.2013
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 285, Issue 1, Pages S169–S182
DOI: https://doi.org/10.1134/S0081543814050198
Bibliographic databases:
Document Type: Article
UDC: 512.54+519.17+548.1
Language: Russian
Citation: V. I. Trofimov, “The finiteness of the number of symmetrical 2-extensions of the dd-dimensional lattice and similar graphs”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 3, 2013, 290–303; Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S169–S182
Citation in format AMSBIB
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\paper The finiteness of the number of symmetrical 2-extensions of the $d$-dimensional lattice and similar graphs
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\vol 19
\issue 3
\pages 290--303
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\issue , suppl. 1
\pages S169--S182
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Linking options:
  • https://www.mathnet.ru/eng/timm988
  • https://www.mathnet.ru/eng/timm/v19/i3/p290
    • This publication is cited in the following 5 articles:
    1. Vladimir L. Averbukh, Natalya V. Averbukh, Pavel Vasev, Ilya I. Gvozdarev, Georgy I. Levchuk, Ilya Starodubtsev, Majid Forghani, 2019 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), 2019, 0786  crossref
    2. E. A. Konovalchik, K. V. Kostousov, “Simmetricheskie 22-rasshireniya 22-mernoi reshetki. II”, Tr. IMM UrO RAN, 23, no. 4, 2017, 192–211  mathnet  crossref  elib
    3. E. A. Konovalchik, K. V. Kostousov, “Simmetricheskie 2-rasshireniya 2-mernoi reshetki. I”, Tr. IMM UrO RAN, 22, no. 1, 2016, 159–179  mathnet  mathscinet  elib
    4. V. I. Trofimov, “The finiteness of the number of symmetrical extensions of a locally finite tree by a finite graph”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 168–173  mathnet  crossref  mathscinet  isi  elib
    5. V. I. Trofimov, “Some remarks on symmetrical extensions of graphs”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 199–208  mathnet  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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