The largest number of faces in a simple connected maximal planar graph with 100 vertices is :

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NIELIT Scientific Assistant CS 5 Dec 2021 Official Paper
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  1. 200 
  2. 198 
  3. 196 
  4. 96

Answer (Detailed Solution Below)

Option 3 : 196 
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Concept:

For a simple connected maximal planar graph with n vertices:

The graph is a triangulation, meaning every face (except possibly the outer one) is a triangle.

In such graphs, the number of edges e is given by:

e=3n6

Using Euler's formula:

ne+f=2

Given:

n=100

So, number of edges:

e=3(100)6=294

Now, apply Euler's formula to find faces:

f=2n+e=2100+294=196

Final Answer:196

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