Computer Science Engineering (CSE) Exam  >  Computer Science Engineering (CSE) Questions  >  In a weighted graph, assume that the shortest... Start Learning for Free
In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.
  • a)
    Yes
  • b)
    No
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a weighted graph, assume that the shortest path from a source '...
See the following counterexample. There are 4 edges s-a, a-b, b-t and s-t of wights 1, 1, 1 and 4 respectively. The shortest path from s to t is s-a, a-b, b-t. IF we increase weight of every edge by 1, the shortest path changes to s-t.
View all questions of this test
Most Upvoted Answer
In a weighted graph, assume that the shortest path from a source '...
Shortest path algorithm in a weighted graph

In a weighted graph, the shortest path between two vertices is calculated using various algorithms such as Dijkstra's algorithm or Bellman-Ford algorithm. These algorithms consider the weights of the edges to determine the shortest path.

Increasing the weight of every edge by 1

Now, let's consider the scenario where we increase the weight of every edge in the graph by 1.

Impact on the shortest path

The statement claims that the shortest path remains the same even after increasing the weight of every edge by 1. However, this statement is false. Increasing the weight of every edge in the graph by 1 will indeed affect the shortest path.

Proof by contradiction

To prove this, let's consider a simple example. Suppose we have a weighted graph with three vertices A, B, and C, where the edge weights are as follows:

- Edge AB: weight 1
- Edge BC: weight 2

The shortest path from A to C is AC, with a total weight of 3. Now, if we increase the weight of every edge by 1, the new weights become:

- Edge AB: weight 2
- Edge BC: weight 3

In this case, the shortest path from A to C will be different. The new shortest path will be AB + BC, with a total weight of 5.

This example demonstrates that increasing the weight of every edge by 1 can change the shortest path in a weighted graph. Therefore, the statement is false.
Explore Courses for Computer Science Engineering (CSE) exam

Top Courses for Computer Science Engineering (CSE)

In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.a)Yesb)NoCorrect answer is option 'B'. Can you explain this answer?
Question Description
In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.a)Yesb)NoCorrect answer is option 'B'. 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 In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.a)Yesb)NoCorrect answer is option 'B'. 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 In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.a)Yesb)NoCorrect answer is option 'B'. Can you explain this answer?.
Solutions for In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.a)Yesb)NoCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE). Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.a)Yesb)NoCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.a)Yesb)NoCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.a)Yesb)NoCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.a)Yesb)NoCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice In a weighted graph, assume that the shortest path from a source 's' to a destination 't' is correctly calculated using a shortest path algorithm. Is the following statement true? If we increase weight of every edge by 1, the shortest path always remains same.a)Yesb)NoCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
Explore Courses for Computer Science Engineering (CSE) exam

Top Courses for Computer Science Engineering (CSE)

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev