You are running Kosaraju’s algorithm to find the SCCs of a directed graph. During the first DFS on the original directed graph 𝐺 , you record finishing times 𝑓 [ 𝑣 ] for all vertices. You then process vertices in decreasing order of finishing times when running the second DFS on the transpose graph .   Which of the following statements accurately describe the behavior and meaning of these timings?  多项选择题

A

The vertex with the largest finishing time belongs to a “sink” SCC in the condensation graph

B

The second DFS, when started from the vertex with the largest finishing time, visits exactly one SCC and no others.

C

The second DFS must process vertices in decreasing order of finishing times in order to guarantee correctness of Kosaraju’s algorithm on all directed graphs.

D

Running the second DFS on G instead of GT would still correctly identify SCCs.

E

The vertex with the smallest finishing time belongs to a “source” SCC in the condensation graph .

F

If there is an edge from SCC C1 to SCC C2 in GSCC, then the maximum finishing time in C1 must be greater than the maximum finishing time in C2.

G

Kosaraju’s algorithm requires O(V2) time due to transposing the adjacency matrix.

H

The vertex with the largest finishing time in the first DFS always belongs to a source SCC in the condensation graph

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