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Difference between Spanning tree and Minimal Spanning Tree

Spanning Tree
A spanning tree of a connected, undirected graph G can also be defined as a maximal set of edges of G that contains no cycle, or as a minimal set of edges that connect all vertices.


A sub-graph T of a connected graph G(V,E) is called a Spanning Tree if T is a tree and if T includes every vertex of G i.e. V(T)=V(G).
If |V|=n and |E|=m, then the spanning tree of G must have n vertices and hence n-1 edges.
The resultant spanning ensure that the graph remain connected and further there is no circuit in it.


Two algorithms for finding a spanning tree are BFS (Breadth First Search) and DFS (Depth First Search).


Minimum Spanning Tree
A minimum spanning tree (MST) or minimum weight spanning tree is then a spanning tree with weight less than or equal to the weight of every other spanning tree.


Two algorithms commonly used, Prim's algorithm and Kruskal's algorithm.


Note:- Difference between Spanning tree and Minimal Spanning Tree is that 
          Spanning Tree is applicable for Graphs without Weights.
          Minimal Spanning Tree is applicable for Weighted Graphs



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