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

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NIELIT Scientific Assistant IT 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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Detailed Solution

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The correct answer is option 3: 196

Key Points

  • A maximal planar graph is a planar graph in which no more edges can be added without violating planarity.
  • In a maximal planar graph with vertices:
    • Number of edges =
    • From Euler’s formula:
  • Given
  • So, edges
  • Apply Euler's formula:

Additional Information

  • This maximum occurs because all faces in a maximal planar graph are triangles.
  • Each triangle shares edges with others, making the total number of faces dependent on total edges and vertices.

Hence, the correct answer is: option 3: 196

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Latest NIELIT Scientific Assistant Updates

Last updated on Jun 26, 2025

-> NIELIT Scientific Assistant admit card 2025 has been released. 

-> NIELIT Scientific Assistant city intimation slip 2025 has been released at the official website.

-> NIELIT Scientific Assistant exam 2025 is scheduled to be conducted on June 28. 

-> A total number of 113 revised vacancies have been announced for the post of Scientific Assistant in Computer Science (CS), Information Technology (IT), and Electronics & Communication (EC) streams.

-> Online application form, last date has been extended up to from 17th April 2025.

->The NIELT has revised the Essential Qualifications for the post of Scientific Assistant. Candidates must possess (M.Sc.)/ (MS)/ (MCA) / (B.E.)/ (B.Tech) in relevant disciplines.

 

-> The NIELIT Scientific Assistant 2025 Notification has been released by the National Institute of Electronics and Information Technology (NIELIT).

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