Prove or disprove the following for a weighted graph G = (V, E), where V = {v0,

Question:

Prove or disprove the following for a weighted graph G = (V, E), where V = {v0, v1, v2, .. . , vn] and e1 ∈ E with wt(e1) < wt(e) for all e ∈ E, e ≠ e1. If Dijkstra's algorithm is applied to G, and the shortest distance d(v0, vt) is computed for each vertex vt, 1 < i < n, then there exists a vertex vj for some 1 < j < n, where the edge e1 is used in the shortest path from no to .