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Title:Uporaba simetrijskih grafov pri konveksnih poliedrih
Authors:Kovič, Jurij (Author)
Pisanski, Tomaž (Co-mentor)
Files:URL http://www.famnit.upr.si/files/zakljucna_dela_repo/73
 
Language:Slovenian
Work type:Dissertation
Tipology:2.08 - Doctoral Dissertation
Organization:FAMNIT - Faculty of Mathematics, Science and Information Technologies
Abstract:Grafe praporov in simetrijske grafe, ki so jih odkrili okrog leta 1980, so doslej uporabljali predvsem za klasifikacijo zemljevidov - to je grafov, celično vloženih v kompaktne ploskve. Namen te disertacije je prikazati nekaj razširitev njihove uporabe. V prvem delu disertacije uporabimo simetrijske grafe pri klasifikaciji poliedrov z regularnimi poligonskimi ali zvezdastimi lici. Podamo tudi karakterizacijo teh poliedrov z minimalnim številom parametrov. V drugem delu disertacije na podoben način klasificiramo molekule,sestavljene iz pravilnih šestkotniških gradnikov, pri čemer upoštevamo tudi njihove točkovne grupe. V tretjem delu disertacije pojem simetrijskih grafov razširimo na hiperzemljevide in geometrijske konfiguracije, nazadnje pa tudi na sferne poliedre in sferne molekule.
Keywords:polieder, graf praporov, simetrijski graf, simetrijska grupa
Year of publishing:2013
Publisher:J. Kovič]
Number of pages:VII, 121 str.
Place:[S. l.
UDC:519.17:514.172.4(043.3)
COBISS_ID:1024512084 Link is opened in a new window
Views:1205
Downloads:23
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Secondary language

Language:English
Abstract:Flag graphs and symmetry-type graphs, discovered around 1980, were used in the past mostly for the classification of maps - i.e. graphs, cellularly embedded into compact surfaces. The purpose of this work is to demonstrate some extensions of their application. In the first part of this work a similar classification of polyhedra with regular faces is given. We present also a characterization of these polyhedra by minimal number of parameters. In the second part of the dissertation we classify in a similar manner the class of molecules, made of regular hexagons, considering also their point groups. In the third part of this work we extend the definition of symmetry-type graphs to hypermaps and geometrical configurations, and finally to spherical polyhedra and spherical molecules.
Keywords:polyhedron, flag-graph, symmetry-type graph, symmetry group

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