create a minimum spanning tree using kruskals algorithm. what is the total minimum length of the spanning…

Explanation:

Step1: Sort edges by weight

Sort all the edges in the graph in ascending order of their weights. The edges and their weights are: $(A - C,3),(B - I,2),(F - H,3),(A - B,5),(D - H,5),(B - C,6),(D - F,9),(B - F,8),(C - D,8),(F - I,8),(C - H,11),(D - I,12)$. After sorting: $(B - I,2),(A - C,3),(F - H,3),(A - B,5),(D - H,5),(B - C,6),(C - D,8),(B - F,8),(F - I,8),(D - F,9),(C - H,11),(D - I,12)$.

Step2: Initialize MST

Initialize an empty set to store the edges of the minimum - spanning tree (MST) and a set to keep track of the vertices already included in the MST. Let the MST set be $T={}$ and the vertex set $V={}$.

Step3: Add edges to MST

Start adding edges from the sorted list to the MST as long as they don't form a cycle.

• First edge: $(B - I,2)$, add it to $T$, and add $B$ and $I$ to $V$.
• Second edge: $(A - C,3)$, add it to $T$, and add $A$ and $C$ to $V$.
• Third edge: $(F - H,3)$, add it to $T$, and add $F$ and $H$ to $V$.
• Fourth edge: $(A - B,5)$, add it to $T$ (no cycle formed).
• Fifth edge: $(D - H,5)$, add it to $T$ (no cycle formed).
• Sixth edge: $(B - C,6)$, add it to $T$ (no cycle formed).

Step4: Calculate total weight

Sum up the weights of the edges in the MST. The weights of the edges in the MST are $2 + 3+3 + 5+5 + 6=24$.

Answer:

24