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Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2024, Volume 26, Number 1, Pages 11–19
DOI: https://doi.org/10.15507/2079-6900.26.202401.11-19
(Mi svmo874)
 

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

On linear spaces of bipartite graphs

V. E. Alekseev, D. V. Zakharovaa

a National Research Lobachevsky State University of Nizhny Novgorod
Full-text PDF (278 kB) Citations (1)
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Abstract: The article considers symmetric linear spaces of bipartite graphs (SLSBG), i.e. the set of bipartite graphs with fixed lobes closed with respect to the symmetric difference and permutations of vertices in each lobe. The operation of symmetric difference itself is introduced in this work. The paper provides a structural description of all SLSBG. Symmetric linear spaces of bipartite graphs are divided into trivial (four SLSBG) and nontrivial. Non-trivial ones, in turn, are divided into two families. The first is C-series consisting only of bicomplete graphs, i.e. graphs that are a disjunct union of two complete bipartite graphs graph wings). The second family is D-series that includes graphs in which the degrees of vertices in one lobe have the same parity, and in the other lobe these degrees may be arbitrary. It is proved that every SLSBG of the D-series coincides with one of nine sets defined by the parity of the vertices’ degrees. For the SLSBG of the C-series it is obtained that every two-sided SLSBG (i.e., containing graphs whose both wings have nonempty lobes) is the intersection of the set of all bicomplete graphs with the set of all graphs with an even number of edges or with any space of the D-series.
Keywords: graph, linear spaces of graphs, bipartite graph, graph isomorphism, symmetric difference of graphs
Received: 11.01.2024
Accepted: 27.02.2024
Document Type: Article
UDC: 519.17
MSC: Primary 05C30; Secondary 05C60, 05C75
Language: Russian
Citation: V. E. Alekseev, D. V. Zakharova, “On linear spaces of bipartite graphs”, Zhurnal SVMO, 26:1 (2024), 11–19
Citation in format AMSBIB
\Bibitem{AleZak24}
\by V.~E.~Alekseev, D.~V.~Zakharova
\paper On linear spaces of bipartite graphs
\jour Zhurnal SVMO
\yr 2024
\vol 26
\issue 1
\pages 11--19
\mathnet{http://mi.mathnet.ru/svmo874}
\crossref{https://doi.org/10.15507/2079-6900.26.202401.11-19}
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  • https://www.mathnet.ru/eng/svmo/v26/i1/p11
  • This publication is cited in the following 1 articles:
    1. Andrey Anatol'evich Beskov, “The rock band “Sektor Gaza” as a phenomenon of Russian (counter)culture”, Filosofiya i kultura, 2024, no. 6, 123  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
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    Full-text PDF :19
    References:15
     
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