Question $1$: Minimum Spanning Tree

You are provided with a map of a newly discovered archipelago consisting of islands

connected by underwater cables. Each cable has a cost associated with it$,$ representing

the difficulty and expense of maintaining that connection. Your task is to design a network

that connects all islands with the minimal possible maintenance cost. Use Kruskal's or

Prim's algorithm to determine the minimum spanning tree $($MST$)$ of the network.

Construct the graph with the given data.

Apply the MST algorithm of your choice to find the minimum maintenance cost to

connect all islands.

Draw the resulting MST and list the connections used.

Explain why the MST you found is minimal and ensure no cycle is formed.