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

Brešar, Boštjan; Klavžar, Sandi; Lipovec, Alenka; Mohar, Bojan

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Title:	Cubic inflation, mirror graphs, regular maps, and partial cubes
Authors:	ID Brešar, Boštjan (Author) ID Klavžar, Sandi (Author) ID Lipovec, Alenka (Author) ID Mohar, Bojan (Author)
Files:	http://www.imfm.si/preprinti/PDF/00888.pdf
Language:	English
Work type:	Not categorized
Organization:	FERI - Faculty of Electrical Engineering and Computer Science
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
Year of publishing:	2003
Number of pages:	str. 1-12
Numbering:	Vol. 41, št. 888
PID:	20.500.12556/DKUM-49370
ISSN:	1318-4865
UDC:	519.17
COBISS.SI-ID:	12592217
NUK URN:	URN:SI:UM:DK:JKY8TO7R
Publication date in DKUM:	10.07.2015
Views:	1381
Downloads:	108
Metadata:
Categories:	Misc.
:	BREŠAR, Boštjan, KLAVŽAR, Sandi, LIPOVEC, Alenka and MOHAR, Bojan, 2003, Cubic inflation, mirror graphs, regular maps, and partial cubes [online]. 2003. [Accessed 19 March 2025]. Retrieved from: http://www.imfm.si/preprinti/PDF/00888.pdf Copy citation

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Secondary language

Language:	Unknown
Title:	Kubična napihovanja, zrcalni grafi, regularni zemljevidi in delne kocke
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.

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