Fibonacci dimension of the resonance graphs of catacondensed benzenoid graphs

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Fibonacci dimension of the resonance graphs of catacondensed benzenoid graphs

The Fibonacci dimension fdim(G) of a graph G was introduced in [1] as the smallest integer d such that G admits an isometric embedding into Γd, 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 catacon...

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The resonance graph of a benzenoid graph G has the 1-factors of G as vertices, two 1-factors being adjacent if their symmetric difference forms the edge set of a hexagon of G. It is proved that the smallest number of elementary cuts that cover a catacondensed benzenoid graph equals the dimension of a largest induced hypercube of its resonance graph.

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ژورنال

عنوان ژورنال: Discrete Applied Mathematics

سال: 2013

ISSN: 0166-218X

DOI: 10.1016/j.dam.2013.03.019