Fibonacci Cubes are the Resonance Graphs of Fibonaccenes

Abstract

Fibonacci cubes were introduced in 1993 and intensively studied afterwards. This paper adds the following theorem to these studies: Fibonacci cubes are precisely the resonance graphs of fibonaccenes. Here fibonaccenes are graphs that appear in chemical graph theory and resonance graphs reect the structure of their perfect matchings. Some consequences of the main result are also listed.