Consider the given graph Its Minimum Cost Spanning Tree is ______

Construct the minimum spanning tree using Kruskal's algorithm:

1. Sort edges by weight (ascending): 1–6 (10), 3–4 (12), 2–7 (14), 2–3 (16), 4–7 (18), 4–5 (22), 5–7 (24), 5–6 (25), 1–2 (28).

2. Pick edges one by one, skipping any that form a cycle:

• Choose 1–6 (10).

• Choose 3–4 (12).

• Choose 2–7 (14).

• Choose 2–3 (16) — this connects the component containing 2 and 7 to the component containing 3 and 4.

• Skip 4–7 (18) because it would create a cycle among {2,3,4,7}.

• Choose 4–5 (22) to attach vertex 5.

• Choose 5–6 (25) to attach {1,6} to the main component (1–6 was already chosen, so this connects that pair to the rest).

The chosen edges are:

• 1–6 (10)

• 3–4 (12)

• 2–7 (14)

• 2–3 (16)

• 4–5 (22)

• 5–6 (25)

Total cost = 10 + 12 + 14 + 16 + 22 + 25 = 99.

Therefore the minimum-cost spanning tree is the tree that contains exactly these edges (total weight 99).