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Lifting graph automorphisms by voltage assignments
Malnič, Aleksander ; Nedela, Roman ; Škoviera, Martin
Problem dviga avtomorfizmov grafov do avtomorfizmov krovnih grafov se obravnava kombinatorično s pomočjo prirejanja napetosti. Zaradi splošnosti in tudi uporabnosti je obravnava razširjena na grafe s ...polpovezavami. To vodi k poenostavitvi in generalizaciji nekaterih znanih rezultatov. Na primer Cayleyevi grafi, vključno tisti z involutoričnimi ter ponavljajočimi se generatorji, so karakterizirani kot regularni krovi nad grafi z enim vozliščem. Pojma navadnih in permutacijskih napetosti sta posplošena in poenoteno zaobsežena v definiciji napetostnega prostora, ki predstavlja ključno pojmovno orodje pri kombinatorični obravnavi problema dviga avtomorfizmov. Poudarek je tudi na strukturi dvigov grup, posebej še na takih razcepnih razširitvah, ki imajo lepo geometrijsko interpretacijo. Prokazan je primer uporabe teh rezultatov v teoriji regularnih zemljevidov na ploskvah.
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