Prove that: order of natural number $d_1 , d_2 , \ldots , d_n$ as descending is a ordering graph if and only if the order was sorted as descending $d_2-1, d_3 -1 , \ldots ,d_d -1,\ldots ,d_n$ be ordering graph. $d_d$ in sequence is d $d_1$. (arrangement=order).
Proof of a graph problem on degree sequence
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graph-theory
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5I'm not sure, but I think you are trying to state the [result of Hakimi for vertex degree sequences](http://en.wikipedia.org/wiki/Degree_(graph_theory)#Degree_sequence). – 2012-10-21