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Let G = (V, E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?
- a)G1 = (V, E1) where E1 = {(u, v)|(u, v) ∉ E}
- b)G2 = (V, E2) where E2 = {(u, v)|(v, u) ∈ E}
- c)G3 = (V, E3) where E3 = {(u, v)| there is a path of length ≤ 2 from u to v in E}
- d)G4 = (V4, E) where V4 is the set of vertices in G which are not isolated
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Let G = (V, E) be a directed graph where V is the set of vertices and ...
In a directed graph G Strongly connected will have a path from each vertex to every other vertex.
If the direction of the edges is reverse, then also graph is strongly connected components as G
If the direction of the edges is reverse, then also graph is strongly connected components as G
Option 2: G2 = (V, E2) where E2 = {(u, v)|(v, u) ∈ E}
In this option G2, edges are reversed and hence it is a strongly connected components as similar to G
So, changing the direction of all the edges, won't change the SCC.
In this option G2, edges are reversed and hence it is a strongly connected components as similar to G
So, changing the direction of all the edges, won't change the SCC.
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Let G = (V, E) be a directed graph where V is the set of vertices and ...
The correct answer is:
c) G3 = (V, E3) where E3 = {(u, v)|(u, v) ∈ E and u ≠ v}
Explanation:
The strongly connected components of a directed graph G are subsets of vertices where there is a directed path from any vertex to any other vertex within the subset.
In G1, every edge in E1 is reversed compared to G. This means that if there is a strongly connected component in G, there will be a strongly connected component in G1, but the edges within that component will be reversed. Thus, G1 does not have the same strongly connected components as G.
In G2, the edges in E2 are a subset of the edges in E. This means that if there is a strongly connected component in G, there will be a strongly connected component in G2, but it is possible that there are additional edges in G that do not belong to any strongly connected component in G2. Thus, G2 does not have the same strongly connected components as G.
In G3, the edges in E3 are the same as the edges in E, but with the restriction that the source and destination vertices are not the same. This means that if there is a strongly connected component in G, there will be a strongly connected component in G3 with the same edges. Thus, G3 has the same strongly connected components as G.
c) G3 = (V, E3) where E3 = {(u, v)|(u, v) ∈ E and u ≠ v}
Explanation:
The strongly connected components of a directed graph G are subsets of vertices where there is a directed path from any vertex to any other vertex within the subset.
In G1, every edge in E1 is reversed compared to G. This means that if there is a strongly connected component in G, there will be a strongly connected component in G1, but the edges within that component will be reversed. Thus, G1 does not have the same strongly connected components as G.
In G2, the edges in E2 are a subset of the edges in E. This means that if there is a strongly connected component in G, there will be a strongly connected component in G2, but it is possible that there are additional edges in G that do not belong to any strongly connected component in G2. Thus, G2 does not have the same strongly connected components as G.
In G3, the edges in E3 are the same as the edges in E, but with the restriction that the source and destination vertices are not the same. This means that if there is a strongly connected component in G, there will be a strongly connected component in G3 with the same edges. Thus, G3 has the same strongly connected components as G.
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Let G = (V, E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?a)G1 = (V, E1) where E1 = {(u, v)|(u, v) ∉ E}b)G2 = (V, E2) where E2 = {(u, v)|(v, u) ∈ E}c)G3 = (V, E3) where E3 = {(u, v)| there is a path of length ≤ 2 from u to v in E}d)G4 = (V4, E) where V4 is the set of vertices in G which are not isolatedCorrect answer is option 'B'. Can you explain this answer?
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Let G = (V, E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?a)G1 = (V, E1) where E1 = {(u, v)|(u, v) ∉ E}b)G2 = (V, E2) where E2 = {(u, v)|(v, u) ∈ E}c)G3 = (V, E3) where E3 = {(u, v)| there is a path of length ≤ 2 from u to v in E}d)G4 = (V4, E) where V4 is the set of vertices in G which are not isolatedCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Let G = (V, E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?a)G1 = (V, E1) where E1 = {(u, v)|(u, v) ∉ E}b)G2 = (V, E2) where E2 = {(u, v)|(v, u) ∈ E}c)G3 = (V, E3) where E3 = {(u, v)| there is a path of length ≤ 2 from u to v in E}d)G4 = (V4, E) where V4 is the set of vertices in G which are not isolatedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G = (V, E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?a)G1 = (V, E1) where E1 = {(u, v)|(u, v) ∉ E}b)G2 = (V, E2) where E2 = {(u, v)|(v, u) ∈ E}c)G3 = (V, E3) where E3 = {(u, v)| there is a path of length ≤ 2 from u to v in E}d)G4 = (V4, E) where V4 is the set of vertices in G which are not isolatedCorrect answer is option 'B'. Can you explain this answer?.
Let G = (V, E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?a)G1 = (V, E1) where E1 = {(u, v)|(u, v) ∉ E}b)G2 = (V, E2) where E2 = {(u, v)|(v, u) ∈ E}c)G3 = (V, E3) where E3 = {(u, v)| there is a path of length ≤ 2 from u to v in E}d)G4 = (V4, E) where V4 is the set of vertices in G which are not isolatedCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Let G = (V, E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?a)G1 = (V, E1) where E1 = {(u, v)|(u, v) ∉ E}b)G2 = (V, E2) where E2 = {(u, v)|(v, u) ∈ E}c)G3 = (V, E3) where E3 = {(u, v)| there is a path of length ≤ 2 from u to v in E}d)G4 = (V4, E) where V4 is the set of vertices in G which are not isolatedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G = (V, E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?a)G1 = (V, E1) where E1 = {(u, v)|(u, v) ∉ E}b)G2 = (V, E2) where E2 = {(u, v)|(v, u) ∈ E}c)G3 = (V, E3) where E3 = {(u, v)| there is a path of length ≤ 2 from u to v in E}d)G4 = (V4, E) where V4 is the set of vertices in G which are not isolatedCorrect answer is option 'B'. Can you explain this answer?.
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