Question
Download Solution PDFThe largest number of faces in a simple connected maximal planar graph with 100 vertices is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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
Last updated on Jul 3, 2025
-> NIELIT Scientific Assistant answer key 2025 has been released at the official website.
-> 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).