Fibonacci dimension of the resonance graphs of catacondensed benzenoid graphs

The Fibonacci dimension fdim(G) of a graph GG was introduced in Cabello et al. (2011) [1] as the smallest integer dd such that GG admits an isometric embedding into ΓdΓd, the dd-dimensional Fibonacci cube. The Fibonacci dimension of the resonance graphs of catacondensed benzenoid systems is studied. This study is inspired by the fact, that the Fibonacci cubes are precisely the resonance graphs of a subclass of the catacondensed benzenoid systems. Our results show that the Fibonacci dimension of the resonance graph of a catacondensed benzenoid system GG depends on the inner dual of GG. Moreover, we show that computing the Fibonacci dimension can be done in linear time for a graph of this class.