(Solution) - Prove or disprove the following for a weighted graph G -(2025 Original AI-Free Solution)

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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 .