The minimum-cost spanning tree produced by applying Kruskal's algorithm will always contain the lowest cost edge of the graph.

Question

Quizplus · Accepted Answer

Kruskal's algorithm starts by sorting all edges in non-decreasing order of their weights. The algorithm then iteratively adds the lowest weight edge to the growing minimum-spanning tree as long as it doesn't create a cycle. Since the edges are added in non-decreasing order of their weights, the lowest cost edge will always be added first, making it a part of the minimum-cost spanning tree.

The Minimum-Cost Spanning Tree Produced by Applying Kruskal's Algorithm Will