The number of distinct minimum spanning trees for the weighted graph below is $\underline{\hspace{1cm}}$

To find the number of distinct Minimum Spanning Trees (MSTs) using Kruskal's algorithm:

1. Edges of weight 1:

   • There are 5 edges of weight 1 in the graph (4 in the left subcomponent and 1 in the right triangle).

   • These edges do not form any cycles among themselves, so all 5 edges with weight 1 must be included in every MST.

2. Edges of weight 2:

   • The connected components formed after selecting all weight-1 edges need to be connected using edges of weight 2 without creating cycles.

   • The bridge between the two components has a single connecting path using weight-2 edges.

   • In the right-hand triangle, with the weight-1 edge already chosen, we have a choice of weight-2 edges to complete the connections.

   • In the left component, there are 3 distinct independent choices to connect the remaining vertices using weight-2 edges.

   • In total, there are $3 \times 2 = 6$ distinct combinations of weight-2 edges that span all vertices while maintaining minimum total weight.

Therefore, the number of distinct MSTs is 6.