V članku raziskujemo probleme izomorfizmov posplošenih Cayleyjevih grafov, ki predstavljajo posplošitve tradicionalnih Cayleyjevih grafov. Ugotovimo, da obstajata dve vrsti naravnih izomorfizmov ...posplošenih Cayleyjevih grafov. Raziskujemo tudi GCI-grupe posplošenih Cayleyjevih grafov in Cayleyjeve regresije nekaterih grup. Predvsem pokažemo, da je za potenco lihega praštevila ▫$n$▫ grupa ▫$Z_{2n}$▫ (oz. ▫$D_{2n}$▫) zožena GCI-grupa, če je ▫$D_{2n}$▫ (oz. ▫$Z_{2n}$▫) CI-grupa. Pokažemo tudi, da je ciklična grupa reda ▫$2^n$▫ 4-kvazi-Cayleyjeva regresija, če in samo če je ▫$n = 3$▫.
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