Fibonacci dimension of the resonance graphs of catacondensed benzenoid graphs
The Fibonacci dimension fdim ( G ) of a graph G G was introduced in Cabello etal. (2011)[1] as the smallest integer d d such that G G admits an isometric embedding into ?d ? d , the d d -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 G G depends on the inner dual of G G . Moreover, we show that computing the Fibonacci dimension can be done in linear time for a graph of this class.
fibonacci dimension resonance graph catacondensed benzenoid system algorithm