From my limited knowledge doesn’t the child have to be under 24 and a fulltime student to be claimed as a dependent on parent tax return? So I think they could rightfully claim an exemption for him in 2013 because he graduated that year, but not for 2014.
And I agree with 4kidsdad, if the parents (or someone else) is eligible to claim child as a dependent, they cannot claim the exemption for themselves.