Planar Graphs and Euler's formula - Questions - Class Mathematics School Portal

Planar Graphs and Euler's formula - Questions

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Question 1

31220

Find the number of vertices \((V)\), edges \((E)\) and faces \((F)\) of the connected planar graph

Answer

\(V=6, E=8, F=4\)

Worked Solution

\begin{align}
&\text{The vertices are } A, B, C, D, E, F=6\\
&\text{The edges are } AB, BD, CD, AC, BF, FE, DF, BE=8\\
&\text{The faces are } ABDC, BDE, BFE \text{ and outside }=4\\
&V-E+F=2 \rightarrow 6-8+4=2
\end{align}

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