Recall that Prim's algorithm starts with an arbitrary vertex and grows the MST by adding the cheapest edge from the tree to a vertex not yet in the tree.

For the given 6-vertex graph, list all edges with their weights and identify the smallest edge to begin the MST construction.

After selecting the first edge, iteratively add the minimum-weight edge that connects a vertex in the current MST to a vertex outside it, ensuring no cycles are formed.