Chemical Graph Theory of Fibonacenes

Fibonacenes (zig-zag unbranched catacondensed benzenoid hydrocarbons) are a class of polycyclic conjugated systems whose molecular graphs possess remarkable properties, often related with the Fibonacci numbers. This article is a review of the chemical graph theory of fibonacenes, with emphasis on their Kekulé–structure–related and Clar–structure–related properties. ————————————————— ∗Supported in part by the Ministry of Science of Slovenia under the grant P1-0297. 0. FIBONACCI NUMBERS The sequence of integers F0, F1, F2, F3, . . . , named after Leonardo Pisano aka Fibonacci (1170–1250), is defined by means of the recurrence relation Fn = Fn−1 + Fn−2 and by means of the initial conditions F0 = 0 ; F1 = 1 . Thus, F2 = 1 , F3 = 2 , F4 = 3 , F5 = 5 , F6 = 8 , F7 = 13 , F8 = 21 , F9 = 34 , F10 = 55 , etc. The mathematical theory of Fibonacci numbers is very interesting and can be found in pertinent books (for instance, in [1, 2]) or in the articles published in the journal “Fibonacci Quarterly”.