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Classification of graphs of diameter $2$ Научная публикация

Журнал Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304
Вых. Данные Год: 2020, Том: 17, Страницы: 502-512 Страниц : 11 DOI: 10.33048/semi.2020.17.031
Ключевые слова graph, diameter 2, diametral vertices, typical graphs, almost all graphs
Авторы Fedoryaeva T.I. 1
Организации
1 Институт математики им. С.Л. Соболева СО РАН

Реферат: The classification of graphs of diameter $2$ by the number of pairs of diametral vertices contained in the graph is designed. All possible values of the parameters $n$ and $k$ are established for which there exists a $n$-vertex graph of diameter $2$ that has exactly $k$ pairs of diametral vertices. As a corollary, the smallest order of these graphs is found. Such graphs with a large number of vertices are also described and counted. In addition, for any fixed integer $k\geq 1$ inside each distinguished class of $n$-vertex graphs of diameter $2$ containing exactly $k$ pairs of diametral vertices, a class of typical graphs is constructed. For the introduced classes, the almost all property is studied for any $k=k(n)$ with the growth restriction under consideration, covering the case of a fixed integer $k\geq 1$. As a consequence, it is proved that it is impossible to limit the number of pairs of diametral vertices by a given fixed integer $k$ in order to obtain almost all graphs of diameter $2$.
Библиографическая ссылка: Fedoryaeva T.I.
Classification of graphs of diameter $2$
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2020. Т.17. С.502-512. DOI: 10.33048/semi.2020.17.031 WOS Scopus РИНЦ MathNet OpenAlex
Даты:
Поступила в редакцию: 19 янв. 2020 г.
Опубликована online: 6 апр. 2020 г.
Идентификаторы БД:
Web of science: WOS:000525533100001
Scopus: 2-s2.0-85129198773
РИНЦ: 44726543
MathNet: rus/semr1226
OpenAlex: W3020593852
Цитирование в БД:
БД Цитирований
OpenAlex 1
Альметрики: