MATH/CSCI Graph Theory Help:) Thank you for helping me I appreciate it, will definitely upvote the correct solution! Please read the question carefully and answer it fully! If you handwrite the solution, please be as legible as possible:) take care and have.a great day!!

a) (20 points) Use the Havel-Hakimi Algorithm to show that d=(6,5,5,4,3,3,2,2,2) is graphic. Your reasoning should be explained in detail along the way at each step of the algorithm. Lack of clarity and coherence will result in point deductions. b) (20 points) Construct a graph with degree sequence exactly d (above in part (a)) by using the set of sequences that resulted from your use of Havel-Hakimi in part (a). All intermediate graphs should be shown, and your constructions and reasoning should be explained in detail at each step along the way. Lack of clarity and coherence will result in point deductions