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Consider an undirected unweighted graph G. Let a breadth-first traversal of G be done starting from a node r. Let d(r, u) and d(r, v) be the lengths of the shortest paths from r to u and v respectively, in G. lf u is visited before v during the breadth-first traversal, which of the following statements is correct? (GATE CS 2001)
  • a)
    d(r, u) < d (r, v)
  • b)
    d(r, u) > d(r, v)
  • c)
    d(r, u) <= d (r, v)
  • d)
    None of the above
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider an undirected unweighted graph G. Let a breadth-first travers...
d(r, u) and d(r, v) will be equal when u and v are at same level, otherwise d(r, u) will be less than d(r, v)
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Most Upvoted Answer
Consider an undirected unweighted graph G. Let a breadth-first travers...
Explanation:

Shortest Path in Breadth-First Traversal:
- In a breadth-first traversal of an undirected unweighted graph, the shortest path from the starting node r to any other node u or v is calculated.

Relationship between d(r, u) and d(r, v):
- If node u is visited before node v during the breadth-first traversal, it implies that u is closer to r than v in terms of the shortest path.
- Therefore, d(r, u) <= d(r,="" v)="" as="" the="" distance="" from="" r="" to="" u="" is="" shorter="" or="" equal="" to="" the="" distance="" from="" r="" to="">

Correct Statement:
- Therefore, the correct statement is d(r, u) = d(r, v) (option 'c') as u is visited before v during the traversal, indicating that both nodes are at the same shortest distance from the starting node r in the graph.
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Consider an undirected unweighted graph G. Let a breadth-first traversal of G be done starting from a node r. Let d(r, u) and d(r, v) be the lengths of the shortest paths from r to u and v respectively, in G. lf u is visited before v during the breadth-first traversal, which of the following statements is correct? (GATE CS 2001)a)d(r, u) < d (r, v)b)d(r, u) > d(r, v)c)d(r, u) <= d (r, v)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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Consider an undirected unweighted graph G. Let a breadth-first traversal of G be done starting from a node r. Let d(r, u) and d(r, v) be the lengths of the shortest paths from r to u and v respectively, in G. lf u is visited before v during the breadth-first traversal, which of the following statements is correct? (GATE CS 2001)a)d(r, u) < d (r, v)b)d(r, u) > d(r, v)c)d(r, u) <= d (r, v)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider an undirected unweighted graph G. Let a breadth-first traversal of G be done starting from a node r. Let d(r, u) and d(r, v) be the lengths of the shortest paths from r to u and v respectively, in G. lf u is visited before v during the breadth-first traversal, which of the following statements is correct? (GATE CS 2001)a)d(r, u) < d (r, v)b)d(r, u) > d(r, v)c)d(r, u) <= d (r, v)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider an undirected unweighted graph G. Let a breadth-first traversal of G be done starting from a node r. Let d(r, u) and d(r, v) be the lengths of the shortest paths from r to u and v respectively, in G. lf u is visited before v during the breadth-first traversal, which of the following statements is correct? (GATE CS 2001)a)d(r, u) < d (r, v)b)d(r, u) > d(r, v)c)d(r, u) <= d (r, v)d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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