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.
Some common algorithms to find the MST include:
This is a useful FAQ taken from Geeks for Geeks.
Yes, a graph can have multiple minimum spanning trees if there are multiple sets of edges with the same minimum total weight.
No, Kruskal’s algorithm and Prim’s algorithm are designed for undirected graphs only.
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.
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.
Both Kruskal’s and Prim’s algorithms have a time complexity of