Članek obravnava družino I-grafov, ki je poplošitev družine posplošenih Petersenovih grafov. Preučujemo različne lastnosti I-grafov kot so povezanost, dvodelnost, ožina, točkovna tranzitivnost. ...Predstavimo učinkovit test za ugotavljanje izomorfnosti dveh I-grafov samo iz njunih parametrov. Opišemo grupo avtomorfizmov I-grafa ▫$I(n,j,k)$▫. Dvodelni regularni grafi z ožino vsaj 6 so Levijevi grafi simetričnih kombinatoričnih konfiguracij. Obravnavamo konfiguracije, ki jih dobimo iz dvodelnih I-grafov. Izkaže se, da lahko nekatere med njimi realiziramo v ravnini kot ciklične astralne konfiguracije, t.j. geometrijske konfiguracije z največjo možno simetrijo v ravnini.
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