Which of the following are strongly connected components of the above graph.

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BlackTom AI · Accepted Answer

The question asks which of the provided options are strongly connected components (SCCs) of a graph that is referenced as 'the above graph'. Since the actual graph (its vertices and directed edges) is not shown here, we cannot definitively verify which subsets form SCCs. In general, an SCC is a maximal set of vertices such that every vertex in the set can reach every other vertex in the set via directed paths, and no larger set containing it maintains that property.

Option 1: {D,E,F,G}
- To determine if this is an SCC, we would need to confirm that for every pair of vertices among D, E, F, and G there exists a path from the first to the second and from the second back to the first. We also must ensure that adding any other vertex to this set would violate the mutual reachability property, meaning the set is maximal.
- Without the graph, we cannot verify the existence of bi-directional reachability among all pairs, nor whether the set is maximal. Therefore, we cannot confirm this as an SCC.

Option 2: {A,B,C,D,E,F,G,H,I,J,K}
- This is a large candidate set. The key checks would be: (1) Is every vertex in this set reachable from every other vertex within the set? (2) Is the set maximal, i.e., can we add another vertex from the graph to keep the strong connectivity property? If both hold, it is an SCC; if either fails, it is not.
- Again, verification requires the explicit edge structure of the graph. Merely listing many vertices does not guarantee strong connectivity unless the internal reachability criteria and maximality are satisfied in the given graph.

Option 3: {B,I,R,D}
- Similar criteria apply: we must check mutual reachability among B, I, R, and D. If each pair has a directed path in both directions, this subset could be an SCC, provided it is maximal. If any vertex in this subset cannot reach another, or if there exists a way to add another vertex from the graph while preserving mutual reachability, then it would not be an SCC.
- The presence or absence of the vertex R is also relevant; if R has no two-way reachability with some member, the set would fail the SCC condition.

Option 4: {G,K,B,H}
- The same mutual-reachability test applies here: every vertex in {G, K, B, H} must reach every other vertex within the set, and the set must be maximal. If there exists at least one pair with no bi-directional path, or if the set can be expanded by adding another vertex while preserving strong connectivity, it would not be an SCC.

Key takeaway given the missing graph: to properly evaluate each option as an SCC, we would systematically check for (a) pairwise strong reachability among all nodes in the subset, and (b) maximality by ensuring that no outside vertex can be added without breaking the mutual reachability property. Without the edge list or adjacency details, any judgment about which options are SCCs would be speculative. Please provide the graph or its adjacency structure so we can perform the exact verification step by step.

XLMC0202501 Topic 19 Quiz

Which of the following are strongly connected components of the above graph.

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