In act 1 scene 4 What is the connection between Duncan, Malcom and the Prince of Cumberland?
Duncan is the present King of Scotland at the start of the play. Malcolm is his eldest son. This did not automatically entitle him to accession to the throne, but creating him Prince of Cumberland (which Duncan does in Act One) does do so, as the title is only given to the heir, in the same way that the title Prince of Wales is reserved for the heir to the British throne. Malcolm and Duncan are also linked in their suitability for the kingship, possessing the 'kingly virtues', although it could be argued that Duncan is somewhat lacking in the 'good judgement' required, given his misjudgement of both Thanes of Cawdor in the play.
Do you mean the relationship between the three?? If so, well Duncan is the King of Scotland and Malcom is the son of Duncan. Duncan announces Malcom to be the Prince of Cumberland, meaning he is to be the next in line to the Scottish throne. I got this from the character analysis in Macbeth on enotes.