Algebraic Structure Count of Cyclobutadienyl Bridged Polyacenes |
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| Authors: | Darko Babi? Ante Graovac Ivan Gutman |
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| Affiliation: | 1. The “Ruder Bo?kovi?” Institute , HR-41001 Zagreb, POB 1016, Hungary;2. Croatia Institute of Physical Chemistry, Attila Jozsef University , H-6701 Szeged, POB 105, Hungary |
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| Abstract: | Abstract By substitution of the benzene rings in n]phenylenes with polyacene units (all being of the same length) a new class of compounds is obtained. By analogy we call this class n]acenylenes. Beside linear (Xn), we also examine angularly linked acenylenes which might be realized in two extreme ways: by connecting the polyacene units in a strictly spiral way (Yn) or in the so called zig-zag manner (Zn). The recursion formulae for the algebraic structure count (ASC) of Xn, Yn and Zn are derived here, and they read as: ASC(Xn) = (h + 1). ASC(Xn-1)—ASC(Xn-2) ASC(Yn) = h. ASC(Yn-1) + ASC(Yn-2) ASC(Zn) = h. ASC(Zn-1) + ASC(Zn-2) where n denotes the number of polyacene units and h the number of hexagons in each polyacene unit. It is proved that Yn and Zn have equal ASCs. |
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| Keywords: | Algebraic structure count [n]acenylenes [n]phenylenes |
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