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The Second Riddell Relation and Its Consequences

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Abstract

The second Riddell relation relates the generating functions for the number of labeled connected graphs and the number of labeled blocks. We consider the conditions under which this relation is true for a subclass of connected graphs.Under these conditions, the formulas are valid that express the number of graphs from a subclass of labeled connected graphs trough the generating function of their blocks. By way of application, we obtain expressions for the numbers of labeled connected and 2-connected series-parallel graphs.

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Authors and Affiliations

  1. All-Russian Institute for Scientific and Technical Information, ul. Usievicha 20, Moscow, 125190, 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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Russian Text © V.A. Voblyi, 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 1, pp. 20–32.

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Voblyi, V.A. The Second Riddell Relation and Its Consequences. J. Appl. Ind. Math. 13, 168–174 (2019). https://doi.org/10.1134/S1990478919010174

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  • DOI: https://doi.org/10.1134/S1990478919010174

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