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GATE 2014 [Set-2]
April 3, 2025GATE 2014 [Set-1]
April 3, 2025GATE 2014 [Set-2]
| Question 61 |
A cycle on n vertices is isomorphic to its complement. The value of n is _____.
| 5 | |
| 6 | |
| 7 | |
| 8 |
Question 61 Explanation:
Complement of a graph means, we need to remove the existing edges from the graph and place the new edges which were not earlier among the actual graph.
In a cycle of n vertices, each vertex is connected to other two vertices. So each vertex degree is 2.
When we complement it, each vertex will be connected to remaining n-3 vertices ( one is self and two other vertices in actual graph).
As per given question,
n-3 =2
n=5
Cycle of 5 vertices is
Complement of the above graph1 is
Graph1 and Graph2 are complement each other.
So, the value of n is 5.
In a cycle of n vertices, each vertex is connected to other two vertices. So each vertex degree is 2.
When we complement it, each vertex will be connected to remaining n-3 vertices ( one is self and two other vertices in actual graph).
As per given question,
n-3 =2
n=5
Cycle of 5 vertices is
Complement of the above graph1 is
Graph1 and Graph2 are complement each other.
So, the value of n is 5.
Correct Answer: A
Question 61 Explanation:
Complement of a graph means, we need to remove the existing edges from the graph and place the new edges which were not earlier among the actual graph.
In a cycle of n vertices, each vertex is connected to other two vertices. So each vertex degree is 2.
When we complement it, each vertex will be connected to remaining n-3 vertices ( one is self and two other vertices in actual graph).
As per given question,
n-3 =2
n=5
Cycle of 5 vertices is
Complement of the above graph1 is
Graph1 and Graph2 are complement each other.
So, the value of n is 5.
In a cycle of n vertices, each vertex is connected to other two vertices. So each vertex degree is 2.
When we complement it, each vertex will be connected to remaining n-3 vertices ( one is self and two other vertices in actual graph).
As per given question,
n-3 =2
n=5
Cycle of 5 vertices is
Complement of the above graph1 is
Graph1 and Graph2 are complement each other.
So, the value of n is 5.