Question about Strongly Connected Components (SCCs)

Consider a directed graph G=(V,E) 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 GT 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

Comentários

  1. Joao Meidanis14 de setembro de 2025 às 10:36

    Questão interessante. Todas as afirmações me parecem corretas. A resposta seria E, então?

    ResponderExcluir
    Respostas
    1. Mateus Vicente14 de setembro de 2025 às 14:24

      Sim, professor! De acordo com o meu entendimento todas estão certas e eu fiz de propósito para ser a questão E. Posso fazer isso, certo?

      Excluir

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