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

Planar Graphs and Euler's formula - Questions

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Question 1

31221

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

Answer

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

Worked Solution

\begin{align}
&\text{The vertices are } A, B, C, D=4\\
&\text{The edges are } AB, BC, AC, BD, AD, DC=6\\
&\text{The faces are } ABD,BDC,ADC \text{ and outside }=4\\
&\quad \begin{aligned}
V-E+F&=2 \\
4-6+4&=2
\end{aligned}
\end{align}

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