True/False

Question

Which of the following statements related to graphs are True?

Consider a graph with Positive distinct edges

1.If we add a Positive Integer to all edges, then there are chances to get more than one shortest paths between 2 vertices
2.If we add a Positive Integer to all edges, then there are chances to get more than one longest paths between 2 vertices
3.If we add a Negative Integer to all edges, then there are chances to get more than one shortest paths between 2 vertices
4.If we add a Negative Integer to all edges, then there are chances to get more than one longest paths between 2 vertices

Comments

If there is already more than one shortest path, then after addition of same integer to all edges may get less number of shortest path

All options are wrong

---

Let's say that you are interested in the path between A to C

You add 2 to all the edges. In this case, we get 2 different paths with same weight.

---

All options are wrong

In the Question, He is interested in "chances/possibility".  

Answer 1

1. True :

Take a Triangle graph, with edge weights $2,3,6$. Now add $1$ to all the edges.

2 : True :

Take a Triangle graph, with edge weights $2,3,6$. Now add $1$ to all the edges.

3. True :

Take a Triangle graph, with edge weights $4,5,8$. Now add $-1$ to all the edges.

4. True :

Take a Triangle graph, with edge weights $4,5,8$. Now add $-1$ to all the edges.