Solution

Using Kruskal's algorithm, we select edges in increasing order of weights, without forming a cycle.

From the graph, the selected edge weights are:

$1,1,1,2,2,2,3,4$

Since the graph has $9$ vertices, the minimum spanning tree must have

$9-1=8$ edges.

Now, total weight of MST is

$1+1+1+2+2+2+3+4$

$=16$

Therefore, the weight of the minimum spanning tree is

$16$