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From a directed graph G, we can detect three strongly connected components (SCC), named as C1, C2, and C3. Which one(s) of the following statements are always correct? (1) If we perform depth-first (DFS) algorithm only inside C1, i.e. DFS(C1), there always exists back edge in C1. (2) If we perform depth-first (DFS) algorithm in the whole graph G, the in-between edge (x, y) [where x is from C1, and y is from C2] must be a cross edge. (3) Procedure DFS(G) will finally generate three trees in the depth-first forest. (4) Any edges in-between C1 and C2, C2 and C3, C1 and C3 cannot form big loops/cycles. (5) In the SCC graph, there might be multiple paths connecting from C1 to C2, but they need to be in the same direction.

From a directed graph G, we can detect three strongly connected components (SCC), named as C1, C2, and C3. Which one(s) of the following statements are always correct? (1) If we perform depth-first (DFS) algorithm only inside C1, i.e. DFS(C1), there always exists back edge in C1. (2) If we perform depth-first (DFS) algorithm in the whole graph G, the in-between edge (x, y) [where x is from C1, and y is from C2] must be a cross edge. (3) Procedure DFS(G) will finally generate three trees in the depth-first forest. (4) Any edges in-between C1 and C2, C2 and C3, C1 and C3 cannot form big loops/cycles. (5) In the SCC graph, there might be multiple paths connecting from C1 to C2, but they need to be in the same direction.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Incorrect Question 9 From a directed graph G, we can detect three strongly connected components (SCC), named as C1, C2, and C3. Which one(s) of the following statements are always correct? (1) If we perform depth-first (DFS) algorithm only inside C1, i.e. DFS(C1), there always exists back edge in C1. (2) If we perform depth-first (DFS) algorithm in the whole graph G, the in-between edge (x, y) [where x is from C1, and y is from C2] must be a cross edge. (3) Procedure DFS(G) will finally generate three trees in the depth-first forest. (4) Any edges in-between C1 and C2, C2 and C3, C1 and C3 cannot form big loops/cycles. (5) In the SCC graph, there might be multiple paths connecting from C1 to C2, but they need to be in the same direction. O (1) (2) (3) (4) (5)
Transcribed Image Text:Incorrect Question 9 From a directed graph G, we can detect three strongly connected components (SCC), named as C1, C2, and C3. Which one(s) of the following statements are always correct? (1) If we perform depth-first (DFS) algorithm only inside C1, i.e. DFS(C1), there always exists back edge in C1. (2) If we perform depth-first (DFS) algorithm in the whole graph G, the in-between edge (x, y) [where x is from C1, and y is from C2] must be a cross edge. (3) Procedure DFS(G) will finally generate three trees in the depth-first forest. (4) Any edges in-between C1 and C2, C2 and C3, C1 and C3 cannot form big loops/cycles. (5) In the SCC graph, there might be multiple paths connecting from C1 to C2, but they need to be in the same direction. O (1) (2) (3) (4) (5)
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