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English version:
Journal of Applied and Industrial Mathematics, 2016, 10:2, 302-310

Volume 23, No 2, 2016, P. 5-20

UDC 519.175.3
V. A. Voblyi
Enumeration of labeled connected graphs with given order and number of edges

Abstract:
We deduce a new formula for the number of labeled connected graphs with a given order and number of edges in terms of the block generating function. Applying this formula, we exactly and asymptotically enumerate cacti with given order and cyclomatic number.
Tab. 1, bibliogr. 22.

Keywords: enumeration, labeled graph, block, cactus, asymptotics.

DOI: 10.17377/daio.2016.23.501

Vitali A. Voblyi 1
1. Bauman Moscow State University,
5 2nd Baumanskaya St., 105005, Moscow, Russia
e-mail: vitvobl@yandex.ru

Received 13 July 2015
Revised 14 December 2015

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