Minimum Spanning Tree

[Nomadyb]

Explain the shortest way to create a new MST that occurs when adding a new node and Edge weight, without touching the nodes and edge weights of the existing MST that we have

[Ghideon]

3 hours ago, Nomadyb said:

Explain the shortest way to create a new MST that occurs when adding a new node and Edge weight, without touching the nodes and edge weights of the existing MST that we have

The question is slightly ambiguous. A MST is per definition the "shortest way" to connect all nodes. What does "without touching" mean? The algorithm must be able to visit edges in the existing MST and if required remove one edge (the new edge or some other edge) otherwise there will be a cycle in the graph and hence not a tree. 

Note that the question seems like a typical homework task and if that is the case this forums has specific rules that apply.