Planarity by redrawing

Questions asking to demonstrate planarity by redrawing a graph with no crossing edges.

3 questions · Easy -1.2

7.02f Bipartite test: colouring argument
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Edexcel D1 Q1
6 marks Easy -1.2
  1. Make plane drawings of each of the graphs shown in Figure 1. Graph 1 \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{e1fd42f7-c97c-4bf2-92d3-69afc8bb6e29-02_1155_664_278_529} \captionsetup{labelformat=empty} \caption{Fig. 1}
    \end{figure}
  2. State the name given to Graph 1 and write down the features that identify it.
  3. State, with a reason, whether it is possible to add further arcs to Graph 2 such that it remains a simple connected graph. No further vertices may be added.
    (1 mark)
AQA Further AS Paper 2 Discrete 2022 June Q5
3 marks Moderate -0.5
5
  1. A connected planar graph has 9 vertices, 20 edges and \(f\) faces. Use Euler's formula for connected planar graphs to find \(f\) 5
  2. 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}
Edexcel D1 2007 June Q1
Easy -1.8
Explain what is meant by a planar graph. (Total 2 marks)