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Section 2.3

1. Exercise 2.31: Prove that a sequence \(d_1,d_2,\cdots,d_n\) is graphical if and only if the sequence \(n-d_1-1,n-d_2-1,\cdots,n-d_n-1\) is graphical (after the suitable reordering).
2. Exercise 2.34:
   1. Determine for which integers \(x\), if any, the sequence \(7,6,5,4,3,2,1,x\) is graphical. You may need to reposition \(x\) to make sure the sequence is non-decreasing. Remember that you can also use the first theorem of graph theory to exclude some possible values without much work.
   2. For each of the integers \(x\) described above, construct the corresponding graph by following the steps at the beginning of the proof of theorem 2.10.