The graph given in the test case is shown as :
The nodes A,B,C,D and E denote the obvious 1,2,3,4 and 5 node numbers.
The starting node is A or 1 (in the given test case)
Applying the Prim's algorithm, edge choices available at first are :
A->B (WT. 3) and A->C (WT. 4) , out of which A->B is chosen (smaller weight of edge).
Now the available choices are :
A->C (WT. 4) , B->C (WT. 5) , B->E (WT. 2) and B->D (WT. 6) , out of which B->E is chosen by the algorithm.
Following the same method of the algorithm, the next chosen edges , sequentially are :
A->C and B->D.
Hence the overall sequence of edges picked up by prims are:
A->B : B->E : A->C : B->D
and Total weight of the hence formed MST is : 15