What is the key attribute of Kruskal's Algorithm?

Kruskal's Algorithm is designed to find the minimum spanning tree (MST) for a connected, undirected graph. The key attribute of the algorithm is that it focuses on adding edges in increasing order of their weights while ensuring that no cycles are formed. This process guarantees that the resulting tree is of minimal weight.

When Kruskal's Algorithm operates, it sorts all the edges in the graph by their weight. Then, it systematically adds the smallest edge to the growing spanning tree, assuming the edge does not create a cycle with the edges already included. This prevents the formation of loops and ensures that all vertices remain connected as the tree grows, eventually leading to the inclusion of all vertices with the minimum total edge weight.

In contrast, other choices illustrate incorrect principles or misunderstandings of how the algorithm functions. For example, the idea of randomly selecting edges or selecting edges based on the highest weight does not align with the systematic, ordered approach of Kruskal's Algorithm. The algorithm does not simply stop adding edges once all edges are included; it specifically needs to stop when there are exactly ( n - 1 ) edges in a tree with ( n ) vertices, ensuring connectivity without redundancy.