
Izv. Saratov Univ. Math. Mech. Inform., 2021, Volume 21, Issue 2, Pages 238–245
(Mi isu889)




Scientific Part
Computer Sciences
The construction of all nonisomorphic minimum vertex extensions of the graph by the method of canonical representatives
M. B. Abrosimov^{a}, I. V. Los'^{a}, S. V. Kostin^{b} ^{a} Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russ
^{b} MIREA – Russian Technological University, 78 Vernadskogo Ave., Moscow 119454, Russia
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.
DOI:
https://doi.org/10.18500/181697912021212238245
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UDC:
519.17 Received: 24.07.2020 Revised: 12.10.2020
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 238245
\mathnet{http://mi.mathnet.ru/isu889}
\crossref{https://doi.org/10.18500/181697912021212238245}
\elib{https://elibrary.ru/item.asp?id=45797877}
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