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In a directed acyclic graph with a source vertex s, the quality-score of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex v other than s, the quality-score of v is defined to be the maximum among the quality-scores of all the paths from s to v. The quality-score of s is assumed to be 1.
The sum of the quality-scores of all vertices on the graph shown above is _______ .
  • a)
    929
  • b)
    81
  • c)
    729
  • d)
    1023
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a directed acyclic graph with a source vertex s, the quality-score ...
Let Q(V) denote the quality-score of vertex V.
Q(S) = 1 (Given)
Q(C) = 1 (S → C)
Q(F) = 1 * 9 (S  → C  → F)
Q(A) = 9 (S  → A)
Q(D) = 9*1 (S  → A  → D)
Q(G) = 9 * 1 * 9 (S  → A  → D  → G)
Q(B) = 9 * 1 (S  → A  → B)
Q(E) = 9 * 1 * 9 (S  → A  → D  → E)
Q(T) = 9*1*9*9 (S  → A  → D  → E → T) 
Sum of quality-score of all vertices,
= 1 + 1 + 9 + 9 + 9 + 81 + 9 + 81 + 729 
= 929 
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In a directed acyclic graph with a source vertex s, the quality-score of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex v other than s, the quality-score of v is defined to be the maximum among the quality-scores of all the paths from s to v. The quality-score of s is assumed to be 1.The sum of the quality-scores of all vertices on the graph shown above is _______ .a)929b)81c)729d)1023Correct answer is option 'A'. Can you explain this answer?
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