Definicijo kartezičnega produkta razširimo na grafe z zankami in pokažemo, da Sabidussi-Vizingov izrek o enolični faktorizaciji povezanih končnih enostavnih grafov še vedno velja v tem kontekstu za ...vse povezane končne grafe z najmanj enim vozliščem brez zanke. Pokažemo tudi, da lahko to faktorizacijo izračunamo v ▫$O(m)$▫ časa, kjer je ▫$m$▫ število povezav danega grafa.
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