Asymptotic approximation for the number of n-vertex graphs of given diameter

Результат исследования: Научные публикации в периодических изданияхстатья

Аннотация

We prove that, for fixed k ≥ 3, the following classes of labeled n-vertex graphs are asymptotically equicardinal: graphs of diameter k, connected graphs of diameter at least k, and (not necessarily connected) graphs with a shortest path of length at least k. An asymptotically exact approximation of the number of such n-vertex graphs is obtained, and an explicit error estimate in the approximation is found. Thus, the estimates are improved for the asymptotic approximation of the number of n-vertex graphs of fixed diameter k earlier obtained by Füredi and Kim. It is shown that almost all graphs of diameter k have a unique pair of diametrical vertices but almost all graphs of diameter 2 have more than one pair of such vertices.

Язык оригиналаанглийский
Страницы (с-по)204-214
Число страниц11
ЖурналJournal of Applied and Industrial Mathematics
Том11
Номер выпуска2
DOI
СостояниеОпубликовано - 1 апр 2017

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