In the spanning tree algorithm, suppose that nodes 1,2 , and 3 are in the connected component at some point in the algorithm; this implies that all arcs between nodes 1,2 , and 3 , if they exist, will have to be in the connected component.

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In the spanning tree algorithm, the goal is to connect all nodes in the graph with the minimum number of edges without creating cycles. If nodes 1, 2, and 3 are already in the same connected component, adding all existing arcs between them would create cycles, which is against the principle of a spanning tree. Only enough arcs to keep them connected (directly or indirectly) are included, not necessarily all possible arcs among them.

In the Spanning Tree Algorithm, Suppose That Nodes 1,2