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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, Volume 21, Issue 2, Pages 238–245
DOI: https://doi.org/10.18500/1816-9791-2021-21-2-238-245
(Mi isu889)
 

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

Scientific Part
Computer Sciences

The construction of all nonisomorphic minimum vertex extensions of the graph by the method of canonical representatives

M. B. Abrosimova, I. V. Los'a, S. V. Kostinb

a Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russ
b MIREA – Russian Technological University, 78 Vernadskogo Ave., Moscow 119454, Russia
Full-text PDF (223 kB) Citations (1)
References:
Abstract: A graph $G = (V, \alpha)$ is called primitive if there exists a natural $k$ such that between any pair of vertices of the graph $G$ there is a route of length $k$. This paper considers undirected graphs with exponent 2. A criterion for the primitivity of a graph with the exponent 2 and a necessary condition are proved. A graph is primitive with the exponent 2 if and only if its diameter is 1 or 2, and each of its edges is included in a triangle. A computational experiment on the construction of all primitive homogeneous graphs with the number of vertices up to 16 and the exponent 2 is described, its results are analyzed. All homogeneous graphs of orders 2, 3, and 4, which are primitive with the exponent 2, are given, and for homogeneous graphs of order 5, the number of primitive graphs with the exponent 2 is determined.
Key words: primitive graphs, exponent of graph, regular graphs.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation FSRR-2020-0006
This work was supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of the state task (project No. FSRR-2020-0006).
Received: 24.07.2020
Revised: 12.10.2020
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: Russian
Citation: M. B. Abrosimov, I. V. Los', S. V. Kostin, “The construction of all nonisomorphic minimum vertex extensions of the graph by the method of canonical representatives”, Izv. Saratov Univ. Math. Mech. Inform., 21:2 (2021), 238–245
Citation in format AMSBIB
\Bibitem{AbrLosKos21}
\by M.~B.~Abrosimov, I.~V.~Los', S.~V.~Kostin
\paper The construction of all nonisomorphic minimum vertex extensions of~the~graph by the method of canonical representatives
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2021
\vol 21
\issue 2
\pages 238--245
\mathnet{http://mi.mathnet.ru/isu889}
\crossref{https://doi.org/10.18500/1816-9791-2021-21-2-238-245}
\elib{https://elibrary.ru/item.asp?id=45797877}
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  • https://www.mathnet.ru/eng/isu889
  • https://www.mathnet.ru/eng/isu/v21/i2/p238
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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    Abstract page:130
    Full-text PDF :30
    References:22
     
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