Cubic inflation, mirror graphs, regular maps, and partial cubes

Boštjan Brešar (Author), Sandi Klavžar (Author), Alenka Lipovec (Author), Bojan Mohar (Author)

Abstract

Kubično napihovanje je operacija, ki transformira 2-celično vložen graf ▫$G$▫ v kubični graf vložen v isto ploskev; njen rezultat lahko opišemo tudi kot dual baricentrične subdivizije grafa ▫$G$▫. Vpeljana sta koncepta zrcalnega in pra-zrcalnega grafa. Platonski grafi so karakterizirani kot (i) pra-zrcalni grafi in kot (ii) ravninski grafi z minimalno stopnjo vsaj tri, katerih kubični napihnjenci so zrcalni grafi. Kot aplikacija je pokazano, da so napihnjeni platonski grafi kubične delne kocke. Konstruiranih je še pet sporadičnih primerov takih grafov.

Keywords

matematika;teorija grafov;vložitve grafov;baricentrična subdivizija;platonski grafi;izometrični podgrafi;hiperkocke;avtomorfizmi grafov.;mathematics;graph theory;graph embeddings;barycentric subdivision;Platonic graphs;isometric subgraphs;hypercubes;graph automorphisms;

Data

Language:	English
Year of publishing:	2003
Typology:	0 - Not set
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	519.17
COBISS:	12592217
ISSN:	1318-4865
Views:	62
Downloads:	10
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Kubična napihovanja, zrcalni grafi, regularni zemljevidi in delne kocke
Secondary abstract:	Cubic inflation is an operation that transforms a 2-cell embedded graph ▫$G$▫ into a cubic graph embedded in the same surface; its result can be described as the dual of the barycentric subdivision of ▫$G$▫. New concepts of mirror amd pre-mirror graphs are also introduced. They give rise to a characterization of Platonic graphs (i) as pre-mirror graphs and (ii) as planar graphs of minimum degree at least three whose cubic inflation is a mirror graph. As an application , the inflated Platonic graphs yield two new prime cubic partial cubes. Five more sporadic examples of such graphs are also constructed.
Secondary keywords:	matematika;teorija grafov;vložitve grafov;baricentrična subdivizija;platonski grafi;izometrični podgrafi;hiperkocke;avtomorfizmi grafov.;
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 1-12
Volume:	ǂVol. ǂ41
Issue:	ǂšt. ǂ888
Chronology:	2003
ID:	66369