Prim's Algorithm and disconnected graph

Question

Consider we are trying to apply prim's algorithm on a disconnected graph. Consider that this disconnected graph has vertices a,b,c and d. Where this vertex d is disconnected. Now I need to check my understanding, if we apply prim's algorithm on this disconnected graph, the algorithm will not reach the vertex d and therefore will return a MST with vertices a,b and c only. So, is this assumption right ?

Answer 1

While it is true that the actual definition of MST applies to connected graphs, you could also say that, for a disconnected graph, a minimum spanning forest is composed of a minimum spanning tree for each connected component.

The problem adds an initial step to isolate each connected sub-graph, and apply Prim's algorithm to each of these.

Answer 2

There's no point in applying a Minimum Spanning Tree on a disconnected graph because by definition it is disconnected and it will not span all the vertices. By definition it is relevant only to connected graphs:

A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected , edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight.