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CENTER AND ITS SPECTRUM OF ALMOST ALL n-VERTEX GRAPHS OF GIVEN DIAMETER Научная публикация

Журнал Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304
Вых. Данные Год: 2021, Том: 18, Номер: 1, Страницы: 511-529 Страниц : 19 DOI: 10.33048/semi.2021.18.037
Ключевые слова almost all graphs; center; central vertices; diameter; diametral vertices; graph; radius; spectrum of center; typical graphs
Авторы Fedoryaeva T.I. 1
Организации
1 Sobolev Institute of Mathematics, 4, KOPTYUGA AVE., Novosibirsk, 630090, Russian Federation

Реферат: We study typical (valid for almost all graphs of a class under consideration) properties of the center and its spectrum (the set of centers cardinalities) for n-vertex graphs of fixed diameter k. The spectrum of the center of all and almost all n-vertex connected graphs is found. The structure of the center of almost all n-vertex graphs of given diameter k is established. For k = 1,2 any vertex is central, while for k > 3 we identified two types of central vertices, which are necessary and sufficient to obtain the centers of almost all such graphs; in addition, centers of constructed typical graphs are found explicitly. It is proved that the center of almost all n-vertex graphs of diameter k has cardinality n — 2 for k = 3, and for k > 4 the spectrum of the center is bounded by an interval of consecutive integers except no more than one value (two values) outside the interval for even diameter k (for odd diameter k) depending on k. For each center cardinality value outside this interval, we calculated an asymptotic fraction of the number of the graphs with such a center. The realizability of the found cardinalities spectrum as the spectrum of the center of typical n-vertex graphs of diameter k is established.
Библиографическая ссылка: Fedoryaeva T.I.
CENTER AND ITS SPECTRUM OF ALMOST ALL n-VERTEX GRAPHS OF GIVEN DIAMETER
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2021. V.18. N1. P.511-529. DOI: 10.33048/semi.2021.18.037 WOS Scopus РИНЦ MathNet OpenAlex
Даты:
Поступила в редакцию: 18 мар. 2021 г.
Опубликована online: 18 мая 2021 г.
Идентификаторы БД:
Web of science: WOS:000651771100001
Scopus: 2-s2.0-85108846053
РИНЦ: 46265228
MathNet: rus/semr1377
OpenAlex: W3200068933
Цитирование в БД:
БД Цитирований
Scopus 1
Web of science 1
РИНЦ 1
OpenAlex 1
Альметрики: