please provide whole process of answer Q1 Use the complement

please provide whole process of answer.

Q1. Use the complementary graphs to show that there exists a graph having degree sequence ( 5 5 5 5 4 4 4).

Solution

Apply Degree Sequence Algorithm to the problem

5555444 m=5, so remove the first term and reduce the next 5 terms
444334   sort in decreasing order
444433   m=4, so remove the first term and reduce the next 4 terms
33323    sort in decreasing order
33332    m=3, so remove the first term and reduce the next 3 terms
2222

We got degree sequence of a graph (2,2,2,2) which is the degree sequence of the cyclic graph C4.
Hence we conclude that the original sequence is also the degree sequence of some graph.