Answer
Showing that if no two edges in a weighted graph have the
same weight, then the edge with least weight incident to
a vertex v is included in every minimum spanning tree.
Work Step by Step
Suppose that edge e is the edge of least weight
incident to vertex v, and suppose that T is a spanning tree that
does not include e.
Add e to T , and delete from the simple circuit formed thereby the other edge of the circuit that contains v.
The result will be a spanning tree of strictly smaller weight
(because the deleted edge has weight greater than the weight of e). This is a contradiction, so T must include e.
