Graf je bi-Cayleyjev graf nad neko grupo, če ta grupa na množici vozlišč grafa deluje semiregularno z dvema orbitama. Naj bo ▫$G$▫ nekomutativna metaciklična ▫$p$▫-grupa za liho praštevilo ▫$p$▫. V ...članku dokažemo, da če je ▫$G$▫ ▫$p$▫-podgrupa Sylowa polne grupe avtomorfizmov ▫$\text{Aut}(\Gamma)$▫ grafa ▫$\Gamma$▫, potem je ▫$G$▫ podgrupa edinka grupe ▫$\text{Aut}(\Gamma)$▫. Na podlagi tega rezultata klasificiramo pol-ločno tranzitivne dvodelne bi-Cayleyjeve grafe nad ▫$G$▫ z valenco manj kot ▫$2p$▫. Klasifikacijo takšnih grafov z valenco 4 sta podala Zhang in Zhou leta 2019. Nadalje pokažemo, da ni nobenih semisimetričnih ali ločno tranzitivnih dvodelnih bi-Cayleyjevih grafov nad ▫$G$▫, ki bi imeli valenco manjšo od ▫$p$▫.
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