use kruskals algorithm to find the minimum spanning tree for the weighted graph. give the total weight of…

Explanation:

Step1: List edges by weight

Sort all the edges of the graph in ascending - order of their weights: $(D, E)$ with weight $3$, $(F, I)$ with weight $12$, $(F, G)$ with weight $11$, $(E, F)$ with weight $15$, $(A, D)$ with weight $3$, $(E, H)$ with weight $14$, $(I, J)$ with weight $18$, $(F, J)$ with weight $13$, $(B, E)$ with weight $16$, $(C, F)$ with weight $19$, $(C, G)$ with weight $10$, $(A, B)$ with weight $6$, $(B, C)$ with weight $23$, $(D, H)$ with weight $8$, $(E, I)$ with weight $17$, $(H, I)$ with weight $21$, $(I, J)$ with weight $18$, $(G, J)$ with weight $22$, $(D, H)$ with weight $8$, $(H, I)$ with weight $21$.

Step2: Select edges for MST

Start adding edges to the minimum - spanning tree (MST) as long as they don't create a cycle.

1. First, add $(D, E)$ with weight $3$.
2. Then add $(C, G)$ with weight $10$.
3. Then add $(F, G)$ with weight $11$.
4. Then add $(F, I)$ with weight $12$.
5. Then add $(F, J)$ with weight $13$.
6. Then add $(E, F)$ with weight $15$.
7. Then add $(B, E)$ with weight $16$.
8. Then add $(A, D)$ with weight $3$.
9. Then add $(E, H)$ with weight $14$.

Step3: Calculate total weight

Sum the weights of the edges in the MST: $3 + 10+11 + 12+13+15+16+3+14=97$.

Step4: Identify the shape

Based on the edges selected in the MST, we can identify the correct shape among the options. (The actual identification of the shape requires visual comparison of the constructed MST with the given options, but the key is to have the correct set of edges in the MST).

Answer:

The total weight of the minimum spanning tree is $97$. (To fully answer the shape - matching part, a visual comparison of the constructed MST with the given options A, B, C, D is needed, but the above steps give the correct MST construction and weight calculation).