Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the following statement:S1: A graph ...
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Consider the following statement:
S1: A graph where all edge weights are distinct can have more than one shortest path between two vertices.
S2: Adding a number on every edge of a graph may change the shortest path between two vertices.
- a)Only S1 is correct.
- b)Only S2 is correct.
- c)Both S1 and S2 are correct.
- d)Neither S1 nor S2 is correct.
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Consider the following statement:S1: A graph where all edge weights ar...
Given,
S1: A graph with distinct edge weights can have more than one shortest path.
Two path (a − d − c) (a − b − c)
S2: Adding a number on every edge of a graph may change the shortest path between two vertices.
As we know,
S2: Consider the graph as shown below:
There are two shortest paths between a and c i.e. (a − b − c) and (a − c). Add 1 to every edge.
Now, only (a−c) is the shortest path thus changed.
Hence, the correct option is (C).
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Community Answer
Consider the following statement:S1: A graph where all edge weights ar...
Shortest Path in Graphs
S1: A graph where all edge weights are distinct can have more than one shortest path between two vertices.
In a graph, a shortest path between two vertices is a path with the minimum sum of edge weights. This means that the total weight of the edges in the shortest path is the smallest possible when compared to all other paths between those two vertices.
Explanation:
- If all edge weights in a graph are distinct, it means that no two edges have the same weight.
- In such a graph, it is possible to have more than one shortest path between two vertices.
- This is because the edge weights are distinct, and there may be multiple combinations of edges with the same total weight that connect the two vertices.
- These different combinations of edges form different paths, all having the same minimum sum of edge weights.
- Therefore, S1 is correct.
S2: Adding a number on every edge of a graph may change the shortest path between two vertices.
In a graph, adding a number to every edge means increasing the weight of each edge by a fixed amount. This can affect the shortest path between two vertices.
Explanation:
- When a number is added to every edge of a graph, the total weight of each edge increases by that number.
- This change in edge weights can alter the shortest path between two vertices.
- The path that was previously the shortest may no longer be the shortest, as the additional weight on the edges can make other paths with different combinations of edges more optimal.
- Therefore, S2 is correct.
Conclusion:
- From the explanations provided, it can be concluded that both S1 and S2 are correct.
- A graph with distinct edge weights can have more than one shortest path between two vertices, and adding a number to every edge of a graph can change the shortest path between two vertices.
S1: A graph where all edge weights are distinct can have more than one shortest path between two vertices.
In a graph, a shortest path between two vertices is a path with the minimum sum of edge weights. This means that the total weight of the edges in the shortest path is the smallest possible when compared to all other paths between those two vertices.
Explanation:
- If all edge weights in a graph are distinct, it means that no two edges have the same weight.
- In such a graph, it is possible to have more than one shortest path between two vertices.
- This is because the edge weights are distinct, and there may be multiple combinations of edges with the same total weight that connect the two vertices.
- These different combinations of edges form different paths, all having the same minimum sum of edge weights.
- Therefore, S1 is correct.
S2: Adding a number on every edge of a graph may change the shortest path between two vertices.
In a graph, adding a number to every edge means increasing the weight of each edge by a fixed amount. This can affect the shortest path between two vertices.
Explanation:
- When a number is added to every edge of a graph, the total weight of each edge increases by that number.
- This change in edge weights can alter the shortest path between two vertices.
- The path that was previously the shortest may no longer be the shortest, as the additional weight on the edges can make other paths with different combinations of edges more optimal.
- Therefore, S2 is correct.
Conclusion:
- From the explanations provided, it can be concluded that both S1 and S2 are correct.
- A graph with distinct edge weights can have more than one shortest path between two vertices, and adding a number to every edge of a graph can change the shortest path between two vertices.
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Consider the following statement:S1: A graph where all edge weights are distinct can have more than one shortest path between two vertices.S2: Adding a number on every edge of a graph may change the shortest path between two vertices.a)Only S1 is correct.b)Only S2 is correct.c)Both S1 and S2 are correct.d)Neither S1 nor S2 is correct.Correct answer is option 'C'. Can you explain this answer?
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