Prim's Algorithm is a greedy approach that is used to find the Minimum Spanning Tree (MST) from a graph.
Let's find out the minimum cost spanning tree for the given graph using Prim's Algorithm.
In the given graph there are no loops and parallel edges are present.
Therefore, no need for any type of removal.
Directly start with selecting any random vertex.
Here, we select Vertex 1 at first.
Finally, we get all the vertices that have been included in the Minimum Spanning Tree, so stop here.
Now, calculate the Cost of the above Minimum Spanning Tree (MST)
$$ Cost\ of\ Minimum\ Spanning\ Tree\ = Sum\ of\ Weights\ of\ all\ edges\ of\ the\ MST $$
$$ = (1, 3) + (1, 2) + (3, 5) + (5, 6) + (5, 4) + (6, 7) + (7, 8) $$ $$ = 6 + 18 + 11 + 4 + 15 + 22 + 34 $$ $$ = 110\ Units $$
Thus, the Minimum Cost of the Spanning Tree for the given graph is 110 Units.