Question: Let G = (V, E) be a connected graph. Form a new graph G' by adding a new vertex w and for each v

Let G = (V, E) be a connected graph. Form a new graph G' by adding a new vertex w and for each v ∈ Van edge connecting w to v. 

(a) Prove that if V[ ≥ 5 and G has an Eulerian path, then G' does not have an Eulerian path. 

(b) Find all connected graphs G for which G and G' both have Eulerian paths.

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