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Planar polycyclic graphs and their Tutte polynomials

We consider several classes of planar polycyclic graphs and derive the 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.

Tutte polynomial ; deletion-contraction invariant ; spanning tree

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