Naj bo ▫$X$▫ končen vozliščno-tranzitven graf valence ▫$d$▫, in naj bo ▫$A$▫ polna grupa avtomorfizmov grafa ▫$X$▫. Potem je ločni tip grafa ▫$X$▫ definiran glede na velikosti orbit delovanja ...stabilizatorja ▫$A_v$▫ danega vozlišča ▫$v$▫ na množici lokov incidentnih z ▫$v$▫. Posebej, ločni tip je razbitje ▫$d$▫ na vsoto ▫$n_1+n_2+\cdots+n_t+(m_1+m_1) + (m_2+m_2) + \cdots + (m_s+m_s)$▫, kjer so ▫$n_1, n_2, \cdots, n_t$▫ velikosti sebi zrcalnih orbit, in ▫$m_1, m_1, m_2, m_2, \cdots, m_s, m_s$▫ velikosti orbit sebi ne-zrcalnih orbit, v padajočem redu. V nedavnem članku so Conder, Pisanski in Žitnik pokazali, da se, z izjemo razbitij ▫$1 + 1$▫ in ▫$(1 + 1)$▫ z valenco 2, vsako takšno razbitje pojavlja kot ločni tip nekega vozliščno tranzitivnega grafa. V tem članku razširimo ta rezultat in pokažemo, da se vsako razbitje, različno od 1, ▫$v1 + 1$▫ and ▫$(1 + 1$)▫, pojavlja kot ločni tip neskončno mnogo povezanih končnih Cayleyjevih grafov z dano valenco ▫$d$▫. Od tod sledi, da za vsak ▫$d > 2$▫ obstaja neskončno mnogo ničelno-simetričnih grafov (ali GRR-ov) valence ▫$d$▫.
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