Planar polycyclic graphs and their Tutte polynomials
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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.
KeywordsSpan Tree Planar Graph Chebyshev Polynomial Span Forest Combinatorial Interpretation
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.
- 1.B. Bollobás, Modern Graph Theory, Graduate Texts in Mathematics 184. (Springer, Berlin, 1998)Google Scholar
- 2.S.J. Cyvin, I. Gutman Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry 46, (Springer, New York, 1988)Google Scholar
- 3.T. Došlić, F. Maløy, Chain hexagonal cacti: matchings and independent sets. Discrete Math. 310, 1176–1190 (2010)Google Scholar
- 4.T. Došlić, M.-S. Litz, Matchings and independent sets in polyphenylene chains. MATCH Commun. Math. Comput. Chem. 67, 313–330 (2012)Google Scholar
- 5.G.H. Fath-Tabar, Z. Gholam-Rezaei, A.R. Ashrafi, On the Tutte polynomial of benzenoid chains. Iran. J. Math. Chem. 3, 113–119 (2012)Google Scholar
- 7.The Online Encyclopedia of Integer Sequences, http://oeis.org