# graphic sequence

Prove that the sequence $< d_1, \cdots ,d_n >$ is a graphic sequence if and only if $< n-d_1 -1 , \cdots ,n-d_n -1 >$ is a graphic sequence.

The theorem I am trying to apply is: " The sequence $<d_1 ,\cdots ,d_n>$ is a graphic sequence if and only if the sequence $< d_2-1 , \cdots ,d_{d_1 +1} -1 , \cdots ,d_n >$ is a graphic sequence.

Any help?

Can you expalain it a little more? It is $n - d_1 -1$ the degree of a vertex in the complement graph. –  passenger Feb 29 '12 at 20:45
o.k I understand it , i did some graphs. It is clear now. $< n-d_1 -1 , \cdots ,n-d_n -1 >$ is the graphic sequence of the complement of $G$. Thank you for your time! –  passenger Feb 29 '12 at 20:59