Skip to content
Related Articles
Get the best out of our app
GeeksforGeeks App
Open App

Related Articles

GATE | GATE-CS-2007 | Question 4

Improve Article
Save Article
Like Article
Improve Article
Save Article
Like Article

Let G be the non-planar graph with the minimum possible number of edges. Then G has


10 edges and 6 vertices


10 edges and 5 vertices 


9 edges and 6 vertices


9 edges and 5 vertices 

Answer: (C)


According to Kuratowski\’s Theorem, a graph is planar if and only if it does not contain any subdivisions of the graphs K5 or K3,3

That means K5 and K3,3 are minimum non-planar graphs. These graphs have 5 vertices with 10 edges in K5 and 6 vertices with 9 edges in K3,3 graph. 
So, graph K5 has minimum vertices and maximum edges than K3,3

Alternative method: 
A plane graph having ‘n’ vertices, cannot have more than ‘2*n-4’ number of edges. Hence using the logic we can derive that for 6 vertices, 8 edges is required to make it a plane graph. So adding one edge to the graph will make it a non planar graph. 

So, 6 vertices and 9 edges is the correct answer. 

So, option (B) is correct.

Quiz of this Question
Please comment below if you find anything wrong in the above post

My Personal Notes arrow_drop_up
Last Updated : 04 Feb, 2020
Like Article
Save Article
Similar Reads