| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Graph Theory Fundamentals |
| Type | Planarity by redrawing |
| Difficulty | Easy -1.2 This is a routine D1 graph theory question requiring students to redraw graphs without crossings (a standard textbook exercise), recall the definition of a complete graph, and apply basic counting of vertices/edges. It tests recall and basic manipulation rather than problem-solving or insight, making it easier than average A-level questions. |
| Spec | 7.02d Complete graphs: K_n and number of arcs7.02l Planar graphs: planarity, subdivision, contraction |
\begin{enumerate}
\item (a) Make plane drawings of each of the graphs shown in Figure 1.
\end{enumerate}
Graph 1
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e1fd42f7-c97c-4bf2-92d3-69afc8bb6e29-02_1155_664_278_529}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
(b) State the name given to Graph 1 and write down the features that identify it.\\
(c) 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)\\
\hfill \mbox{\textit{Edexcel D1 Q1 [6]}}