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!!

Spanning Trees, 40 points. Let G be the graph obtained from K5 by deleting two nonincident edges. (a) (10 points) Assign the weights (1,1,2,2,3,3,4,4) to the edges of G so that the minimum spanning tree of G is unique. Call this graph G1. Be sure to explain in detail why the spanning tree is unique in this case. Your solution should be coherent and precise. Do not leave out any details whatsoever. Write complete sentences. Lack of clarity and precision will result in point deductions. (b) (10 points) Next assign the weights (1,1,2,2,3,3,4,4) to the edges of G in another way so that the minimum spanning tree is not unique. Call this graph G2. Be sure to verify that the spanning tree is not unique in this case. Your solution should be coherent and precise. Do not leave out any details whatsoever. Write complete sentences. Lack of clarity and precision will result in point deductions. (c) (10 points) Run your graph G1 through Prim's Algorithm and give a step-by-step explanation of the output. Your solution should be coherent and precise. Do not leave out any details whatsoever. Write complete sentences. Lack of clarity and precision will result in point deductions. d) (10 points) Run your graph G2 through Kruskal's Algorithm and give a step-by-step explanation of the output. Your solution should be coherent and precise. Do not leave out any details whatsoever. Write complete sentences. Lack of clarity and precision will result in point deductions