Z-transformation graphs of perfect matchings of hexagonal systems
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
Plane elementary bipartite graphs
Discrete Applied Mathematics
Resonance graphs of catacondensed even ring systems are median
Discrete Mathematics
Fibonacci Cubes-A New Interconnection Topology
IEEE Transactions on Parallel and Distributed Systems
Fast Recognition of Fibonacci Cubes
Algorithmica
Resonance Graphs and a Binary Coding for the 1-Factors of Benzenoid Systems
SIAM Journal on Discrete Mathematics
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The Fibonacci dimension fdim(G) of a graph G was introduced in Cabello et al. (2011) [1] as the smallest integer d such that G admits an isometric embedding into @C"d, the 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 depends on the inner dual of G. Moreover, we show that computing the Fibonacci dimension can be done in linear time for a graph of this class.