Question:
Let \( G \) be a simple, unweighted, and undirected graph. A subset of the vertices and edges of \( G \) are shown below.
It is given that \( a - b - c - d \) is a shortest path between \( a \) and \( d \); \( e - f - g - h \) is a shortest path between \( e \) and \( h \); \( a - f - c - h \) is a shortest path between \( a \) and \( h \). Which of the following is/are NOT the edges of \( G \)?
Let \( G \) be a simple, unweighted, and undirected graph. A subset of the vertices and edges of \( G \) are shown below.
It is given that \( a - b - c - d \) is a shortest path between \( a \) and \( d \); \( e - f - g - h \) is a shortest path between \( e \) and \( h \); \( a - f - c - h \) is a shortest path between \( a \) and \( h \). Which of the following is/are NOT the edges of \( G \)?
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For shortest path problems in graphs, analyze given shortest paths carefully to determine missing edges.
Updated On: Feb 3, 2026
- \( (b,d) \)
- \( (b,g) \)
- \( (b,h) \)
- \( (e,g) \)
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The Correct Option is A, C, D
Solution and Explanation
Analyze the shortest paths provided in the problem.
The shortest path from \( a \) to \( d \) is \( a - b - c - d \). This means there is no direct edge between \( b \) and \( d \).
The shortest path from \( e \) to \( h \) is \( e - f - g - h \). This implies that \( e \) and \( g \) are not directly connected.
The shortest path from \( a \) to \( h \) is \( a - f - c - h \), suggesting that \( b \) and \( h \) are not directly connected.
The shortest path from \( a \) to \( d \) is \( a - b - c - d \). This means there is no direct edge between \( b \) and \( d \).
The shortest path from \( e \) to \( h \) is \( e - f - g - h \). This implies that \( e \) and \( g \) are not directly connected.
The shortest path from \( a \) to \( h \) is \( a - f - c - h \), suggesting that \( b \) and \( h \) are not directly connected.
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