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:

\( e = 3n - 6 \)

Using Euler's formula:

\( n - e + f = 2 \)

Given:

\( n = 100 \)

So, number of edges:

\( e = 3(100) - 6 = 294 \)

Now, apply Euler's formula to find faces:

\( f = 2 - n + e = 2 - 100 + 294 = 196 \)

Final Answer:196

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