About NN, father of Constantine 'Dufagan'
Hypothetical father of Constantine and Gillemichael. May or may not have been Mormaer of Fife circa Edgar I and Alexander I.
'Dufagan comes' mentioned in a [possibly] spurious foundation charter for Scone Abbey. [He] has no province name, but he is often [mistakenly] called Mormaer or Earl of Angus because he shares the same name as Dubacan son of Indrechtach - who was the Mormaer of Angus. https://en.wikipedia.org/wiki/Dubacan_of_Angus
Possibly a Fictional Person created to "explain" Gillemichael of Fife's styling himself "Mac duf". The lords of Fife were descendants of King Dubh (Duff, Duffus, d. 967) of the previous royal line, and no other explanation was really necessary. In any case it is not likely that Gillemichael would have belonged to the rival province of Moray.