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 Jun 12, 2025
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