Δικός means nothing on its own. It is always coupled with (μου, του, σου, μας, σας, τους) and is mine, yours, his etc.
Hmmm...I also wrote "the children are mine" and it was counted as correct.
Let me see if I understand. If i just want to say something is someone's, in this case the children are mine, I use the δικά μου, but if I wanted to say more, like My children are..., I would use just μου, without δικά, like Τα παιδιά μου είναι... ?
Is δικά congregated to match τα παιδιά in the sentence? Is δικά plural?