On the Fibonacci dimension of partial cubes

Abstract

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.

Keywords

matematika;teorija grafov;Fibonaccijeva dimenzija;delne kocke;resonančni grafi;benzenoidni sistemi;mathematics;graph theory;Fibonacci dimension;partial cubes;resonance graphs;benzenoid systems;

Data

Language:	English
Year of publishing:	2009
Typology:	0 - Not set
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	519.17
COBISS:	15310681
ISSN:	1318-4865
Views:	34
Downloads:	8
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary keywords:	matematika;teorija grafov;Fibonaccijeva dimenzija;delne kocke;resonančni grafi;benzenoidni sistemi;
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 1-9
Volume:	ǂVol. ǂ47
Issue:	ǂšt. ǂ1104
Chronology:	2009
ID:	1474503