Math Problem Statement
Let G be a plane graph with n vertices, m edges and f faces. Using Euler’s formula, prove that n-m+f=k)G)+1 where k(G) is the number of connected components of G.
Solution
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Math Problem Analysis
Mathematical Concepts
Graph Theory
Euler's Formula
Connected Components
Formulas
Euler's formula: n - m + f = 2 for connected plane graphs
Theorems
Euler's Formula for Planar Graphs
Suitable Grade Level
Advanced High School
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