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Enumeration of labeled connected graphs with given order and size

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Abstract

We deduce a new formula for the number of labeled connected graphs with 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.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005, Russia

    V. A. Voblyi

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  1. V. A. Voblyi
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Correspondence to V. A. Voblyi.

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Original Russian Text © V.A. Voblyi, 2016, published in Diskretnyi Analiz i Issledovanie Operatsii, 2016, Vol. 23, No. 2, pp. 5–20.

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Voblyi, V.A. Enumeration of labeled connected graphs with given order and size. J. Appl. Ind. Math. 10, 302–310 (2016). https://doi.org/10.1134/S1990478916020149

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  • DOI: https://doi.org/10.1134/S1990478916020149

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