Graf ▫$\Gamma$▫ z grupo avtomorfizmov ▫$H$▫, ki deluje polregularno na vozliščih z dvema orbitama se imenuje bi-Cayleyev graf nad grupo ▫$H$▫. Kadar je ▫$H$▫ edinka grupe ▫$\text{Aut}(\Gamma)$▫, ...pravimo da je ▫$\Gamma$▫ normalen graf glede na grupo ▫$H$▫. V tem članku pokažemo, da ima vsaka končna grupa povezan normalen bi-Cayleyev graf. To je izboljšava izreka Arezoomanda in Taerija in daje pozitiven odgovor na vprašanje, omenjeno v literaturi.
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