Prove that the sequence $ \langle d_1, \cdots ,d_n \rangle$ is a graphic sequence if and only if $\langle n-d_1-1, \cdots, n-d_n -1 \rangle$ is a graphic sequence.
The theorem I am trying to apply is: " The sequence $\langle d_1 ,\cdots , d_n\rangle$ is a graphic sequence if and only if the sequence $\langle d_2-1 , \cdots ,d_{d_1 +1} -1 , \cdots ,d_n \rangle $ is a graphic sequence.
Any help?
Thank's in advance!