http://en.wikipedia.org/wiki/Duncan_I_of_Scotland

Donnchad mac Crínáin [2] anglicised as Duncan I, and nicknamed An t-Ilgarach, "the Diseased" or "the Sick"[3] [1] was king of Scotland . He was son of Crínán, hereditary lay abbot of Dunkeld, and Bethóc, daughter of king Malcolm II of Scotland .
Unlike the "King Duncan" of Shakespeare's Macbeth, the historical Duncan appears to have been a young man. He followed his grandfather Malcolm as king after the latter's death on 25 November 1034, without apparent opposition. He may have been Malcolm's acknowledged successor or tánaise as the succession appears to have been uneventful.[4] Earlier histories, following John of Fordun, supposed that Duncan had been king of Strathclyde in his grandfather's lifetime, ruling the former Kingdom of Strathclyde as an appanage. Modern historians discount this idea.[5]
Another claim by Fordun, that Duncan married the sister, daughter or cousin of Sigurd the Dane, Earl of Northumbria, appears to be equally unreliable. An earlier source, a variant of the Chronicle of the Kings of Alba , gives Duncan's wife the Gaelic name Suthen.[6] Whatever his wife's name may have been, Duncan had at least two sons. The eldest, Malcolm III was king from 1057 to 1093, the second Donald III was king afterwards. Máel Muire, Earl of Atholl is a possible third son of Duncan, although this is uncertain.[7]
The early period of Duncan's reign was apparently uneventful, perhaps a consequence of his youth. Macbeth is recorded as his dux, literally duke, but in the context — "dukes of Francia" had half a century before replaced the Carolingian kings of the Franks and in England the over-mighty Godwin of Wessex was called a dux — this suggests that Macbeth was the power behind the throne.[8]
In 1039, Duncan led a large Scots army south to besiege Durham, but the expedition ended in disaster. Duncan survived, but the following year he led an army north into Moray, traditionally seen as Macbeth's domain. There he was killed, at Pitgaveny near Elgin, by his own men led by Macbeth, probably on 14 August 1040.[9]

https://en.wikipedia.org/wiki/Dúnlaing_mac_Muiredaig

Dúnlaing mac Muiredaig was a King of Leinster of the Uí Muiredaig sept of the Uí Dúnlainge branch of the Laigin. This sept had their royal seat at Maistiu in South Kildare. He was the son of Muiredach mac Brain , a previous king.[1] He ruled from 863 to 869.

There is much confusion in the king lists during this period for Leinster. Between 838-871 the title King of Leinster is not recorded in the Annals of Ulster. The death of Dúnlaing is not recorded in this annal but is recorded in other annals.[2] Francis John Byrne suggests that the root of this apparent confusion lay in the fact that the Uí Dúnlainge kings exercised little real authority due to the aggressions of their western neighbour Cerball mac Dúnlainge , King of Osraige. Cerball, while unable to install himself as king of Leinster, was able to prevent any rival king exercising real power there.[3]

In 868 the annals record that the Laigin participated with the Uí Néill of Brega and Norse at the Battle of Cell Ua nDaigri on the Boyne estuary. They were defeated by the high king Áed Findliath .[4] Dúnlaing's name is not mentioned with connection to this event.

His son Ailill mac Dúnlainge was also a King of Leinster. Another son Cairpre mac Dúnlainge was King of Iarthair Liffey or western Liffey.