20.500.12556/DKUM-51805 On the Fibonacci dimension of partial cubes The Fibonacci dimension fdim▫$(G)$▫ of a graph ▫$G$▫ was introduced in [S. Cabello, D. Eppstein and S. Klavžar, The Fibonacci dimension of a graph, submitted] as the smallest integer ▫$d$▫ such that $G$ admits an isometric embedding into ▫$Q_d$▫, the ▫$d$▫-dimensional Fibonacci cube. A somewhat new combinatorial characterization of the Fibonacci dimension is given, which enables more comfortable proofs of some previously known results. In the second part of the paper 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. The main result shows 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. matematika teorija grafov Fibonaccijeva dimenzija delne kocke resonančni grafi benzenoidni sistemi mathematics graph theory Fibonacci dimension partial cubes resonance graphs benzenoid systems true false false Angleški jezik Neznan jezik Delo ni kategorizirano 2015-07-10 15:11:09 2015-07-10 15:11:09 2022-05-30 03:07:28 2019-07-11 07:28:46 2009 0 0 str. 1-9 št. 1104 Vol. 47 2009 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1318-4865 519.17 44310272 15310681 URN:SI:UM:DK:M276KAJO http://www.imfm.si/preprinti/PDF/01104.pdf 1 https://dk.um.si/Dokument.php?lang=slv&id=76365 Fakulteta za naravoslovje in matematiko 0 0 0