Spanning Trees

Let G = (VE) be a connected graph in which each edge (uv$ \in$E has an associated cost C(uv).

Spanning Tree for G is a subgraph of G that it is a free tree connecting all vertices in V. The cost of a spanning tree is the sum of costs on its edges.
Minimum Spanning Tree
An MST of G is a spanning tree of G having a minimum cost.
Spanning Trees
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