On the Fibonacci dimension of partial cubes

Povzetek

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.

Ključne besede

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

Podatki

Jezik:	Angleški jezik
Leto izida:	2009
Tipologija:	0 - Ni določena
Organizacija:	UM FNM - Fakulteta za naravoslovje in matematiko
UDK:	519.17
COBISS:	15310681
ISSN:	1318-4865
Št. ogledov:	34
Št. prenosov:	8
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarne ključne besede:	matematika;teorija grafov;Fibonaccijeva dimenzija;delne kocke;resonančni grafi;benzenoidni sistemi;
URN:	URN:SI:UM:
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	str. 1-9
Letnik:	ǂVol. ǂ47
Zvezek:	ǂšt. ǂ1104
Čas izdaje:	2009
ID:	1474503