Original title: Grupy automorfizmov geometricky reprezentovatel'n'ych grafov
Translated title: Automorphism Groups of Geometrically Represented Graphs
Authors: Zeman, Peter ; Klavík, Pavel (advisor) ; Nedela, Roman (referee)
Document type: Bachelor's theses
Year: 2014
Language: eng
Abstract: [eng] [cze]
In this thesis, we are interested in automorphism groups of classes of graphs with a very strong structure. Probably the first nontrivial result in this direction is from 1869 due to Jordan. He gave a characterization of the class T of the automorphism groups of trees. Surprisingly, automorphism groups of intersection-defined classes of graphs were studied only briefly. Even for deeply studied classes of intersection graphs the structure of their automorphism groups is not well known. We study the problem of reconstruct- ing the automorphism group of a geometric intersection graph from a good knowledge of the structure of its representations. We mainly deal with interval graphs. Interval graphs are intersection graphs of intervals on the real line. They are one of the oldest and most studied classes of geometric intersection graphs. Our main result is that the class T is the same as the class I of the automorphism groups of interval graphs. Moreover, we show for an interval graph how to find a tree with the same automorphism group, and vice versa. 1 V tejto práci skúmame grupy automorfizmov grafov s vel'mi silnou štruktúrou. Pravdepodobne jeden z prvých výsledkov v tomto smere je Jordanova charakterizácia triedy grúp automorfizmov stromov T z roku 1869. Prekvapivo, grupy automorfizmov prienikových grafov boli študované iba vel'mi málo. Aj pre vel'mi pochopené triedy prienikových grafov, je štruktúra ich grúp auto- morfizmov neznáma. Hlavná otázka, ktorou sa zaoberáme je, či sa z dobrej znalosti reprezentácií prienikového grafu geometrických objektov dá zrekonštruovat' jeho grupa automorfizmov. V práci skúmame hlavne intervalové grafy. Intervalové grafy sú prienikové grafy intervalov na reálnej osi. Sú jednou z naj- starších a najviac študovaných tried prienikových grafov. Náš hlavný výsledok ho- vorí, že trieda grúp automorfizmov intervalových grafov I je rovnaká ako trieda grúp automorfizmov stromov T . Navyše ukazujeme postup ako pre daný intervalový graf skonštruovat' strom s rovnakou grupou automorfizmov a tak isto obrátene, pre daný strom skonštruujeme intervalový graf. 1
Keywords: automorphism groups; intersection graphs; interval graphs; representations; grupy automorfismů; intervalové grafy; průnikové grafy; reprezentace

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/71160

Permalink: http://www.nusl.cz/ntk/nusl-458810


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses