Consider the following undirected graph G with
$$V = \{A, B, C, D, E, F, G, H\}$$.
The edges are:
| Edge | Weight |
| :----- | :----- |
| (A, B) | 3 |
| (A, C) | 3 |
| (B, C) | 5 |
| (B, D) | 5 |
| (C, D) | 5 |
| (D, E) | 2 |
| (B, E) | 2 |
| (C, F) | 6 |
| (D, G) | 7 |
| (F, G) | 7 |
| (B, H) | 10 |
| (E, H) | 10 |
(a) Perform Prim's algorithm starting from node A. Show how the MST is constructed, step by step.
(b) Perform Kruskal's algorithm to construct the MST. Specify the order in which edges are considered and which edges are added or rejected.
2.2 Question 2
(a) Determine whether the MST for the graph in Question 1 is unique.
(b) Provide pseudocode for checking whether a weighted undirected graph has a unique MST.