2025-261

Consider a directed graph \(G\) and the Kosaraju-Sharir's algorithm for finding strongly connected components (SCCs). Analyze the following statements:

I. The SCC decomposition of a directed graph is unique, but the particular order in which SCCs are discovered by Kosaraju’s algorithm may depend on the order of adjacency lists.

II. If a directed graph has no back edges in a DFS traversal, then each vertex forms a distinct SCC.

III. If \(G\) is strongly connected, then the second DFS in Kosaraju’s algorithm produces a single tree covering all vertices, regardless of the order of exploration.

IV. The order of vertices given by decreasing finishing times of the first DFS guarantees that the second DFS on the transposed graph \(G^T\)$$discovers one SCC at a time.

Select the correct alternative:

A) Only I and II are correct.
B) Only I and IV are correct.
C) Only I, II and IV are correct.
D) Only I, III and IV are correct.
E) None of the above.

Original idea by: Mateus de Padua Vicente