Minimum Spanning Tree

A minimum spanning tree is the Spanning Tree with the minimum weight among all other spanning trees of a given graph. This is found when given a Connected, Undirected, Weighted graph.

It is also possible for there to be multiple MSTs for a single graph.

Algorithms to find Minimum Spanning Tree

Some common algorithms to find the MST include:

FAQ

This is a useful FAQ taken from Geeks for Geeks.

1. Can there be multiple minimum-spanning trees for a given graph?

Yes, a graph can have multiple minimum spanning trees if there are multiple sets of edges with the same minimum total weight.

2. Can Kruskal’s algorithm and Prim’s algorithm be used for directed graphs?

No, Kruskal’s algorithm and Prim’s algorithm are designed for undirected graphs only.

3. Can a disconnected graph have a minimum spanning tree?

No, a disconnected graph cannot have a spanning tree because it does not span all the vertices. Therefore, it also cannot have a minimum spanning tree.

4. Can a minimum spanning tree be found using Dijkstra’s algorithm?

No, Dijkstra’s algorithm is used to find the shortest path between two vertices in a weighted graph. It is not designed to find a minimum spanning tree.

5. What is the time complexity of Kruskal’s and Prim’s algorithms?

Both Kruskal’s and Prim’s algorithms have a time complexity of  where is the number of edges in the graph.