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Journal of Mathematical Chemistry

, Volume 51, Issue 6, pp 1599–1607 | Cite as

Planar polycyclic graphs and their Tutte polynomials

  • Tomislav DošlićEmail author
Original Paper

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.

Keywords

Span Tree Planar Graph Chebyshev Polynomial Span Forest Combinatorial Interpretation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Civil EngineeringUniversity of ZagrebZagrebCROATIA

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