Math Problem Statement
Solution
For the planar graph shown:
-
Number of interior faces: Count the regions inside the graph that are enclosed by edges. The graph has 3 interior faces.
-
Total number of faces: In a planar graph, the total number of faces includes all interior faces plus the exterior face. Therefore, the graph has 4 faces in total.
-
Euler's formula: Euler's formula for planar graphs is , where is the number of vertices, is the number of edges, and is the number of faces.
For this graph:
- (vertices: A, B, C, D, E, F)
- (edges)
So, substituting into Euler's formula, we get:
-
Faces for another planar graph: Without the graph shown, it’s not possible to calculate how many faces another graph would have without further details.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Planar Graphs
Euler's Formula
Graph Theory
Formulas
Euler's Formula: V - E + F = 2
Theorems
Euler's Formula for Planar Graphs
Suitable Grade Level
Grades 10-12
Related Recommendation
Determining the Number of Faces in a Planar Graph using Euler's Formula
Determine the Number of Faces in a Planar Graph with Euler's Formula
Determining the Number of Faces in a Planar Complete Graph K8
Determine the Number of Faces in a Planar Graph Using Euler's Formula
Calculating Regions (Faces) in a Planar Graph Using Euler's Formula