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Planar polycyclic graphs and their Tutte polynomials

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Abstract

We consider several classes of planar polycyclic graphs and derive recurrences satisfied by their Tutte polynomials. The recurrences are then solved by computing the corresponding generating functions. As a consequence, we obtain values of several chemically and combinatorially interesting enumerative invariants of considered graphs. Some of them can be expressed in terms of values of Chebyshev polynomials of the second kind.

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Acknowledgments

Partial support of the Ministry of Science, Education and Sport of the Republic of Croatia (Grants No. 177-0000000-0884 and 037-0000000-2779) is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Kačićeva 26, 10000 , Zagreb, CROATIA

    Tomislav Došlić

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  1. Tomislav Došlić
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Correspondence to Tomislav Došlić.

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Došlić, T. Planar polycyclic graphs and their Tutte polynomials. J Math Chem 51, 1599–1607 (2013). https://doi.org/10.1007/s10910-013-0167-2

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  • DOI: https://doi.org/10.1007/s10910-013-0167-2

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