Question 5 - A-Level Maths

Exam Board	AQA
Module	Further AS Paper 2 Discrete (Further AS Paper 2 Discrete)
Year	2022
Session	June
Topic	Graph Theory Fundamentals

A connected planar graph has 9 vertices, 20 edges and \(f\) faces. Use Euler's formula for connected planar graphs to find \(f\) 5
The graph \(J\), shown in Figure 1, has 9 vertices and 20 edges. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{ecbeedf5-148e-40ad-b8a2-a7aa3db4a115-09_778_760_440_641}
\end{figure} By redrawing the graph \(J\) using Figure 2, show that \(J\) is planar. \begin{table}[h]
\captionsetup{labelformat=empty} \caption{Figure 2}
\(A\) \(B\) \(C\)
\(\bullet\) \(\bullet\) \(\bullet\)
\(D \bullet\) \(E \bullet\) \(\bullet F\)
\(\bullet\) \(\stackrel { \theta } { H }\) \(\bullet\)
\end{table}