(Solved): Problem 5. Consider the graph K5 (Figure 2) with a weighted adjacency matrix (Table 1). Figure 2 ...

Problem 5. Consider the graph $K_5$ (Figure 2) with a weighted adjacency matrix (Table 1). Figure 2: $K_5$. Table 1: Weighted adjacency matrix. (i) Use Prim's algorithm (start with vertex $a$ ) to find a MST of this graph. Compute its total length. Show steps! (ii) Use Kruskal's algorithm to find a MST of this graph. Compute its total length. Show steps! (iii) Using the MST you calculated in (ii), find a TSP tour of this graph. Compute its total length. (iv) Consider the MST you calculated in (ii). Assume that the weight of $(a,b)$ is a variable, say $\beta$. For what values of $\beta$ will this edge be in this MST?