Znani Petersenov graf ▫$G(5,2)$▫ ima avtomorfizem ▫$\alpha$▫ z dvema enako velikima vozliščnima orbitama. Pravimo, da ▫$\alpha$▫ deluje na množico vozlišč polregularno. Graf, ki dopušča polregularni ...avtomorfizem, pa imenujemo bicirkulant. Izkaže se, da trivalentni bicirkulanti sodijo v štiri razrede. Prikazane so nekatere osnovne lastnosti trivalentnih bicirkulantov in njihova povezava s kombinatoričnimi in geometričnimi konfiguracijami. Omenjene so nekatere analogije s policirkulantno domnevo.
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