| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Graph Theory Fundamentals |
| Type | Vertex degree sequences |
| Difficulty | Easy -1.2 This question tests basic graph theory concepts (degree sequences, connectedness) with straightforward applications of the handshaking lemma. Parts (a)-(b) require simple drawings with no problem-solving, while part (c) involves elementary reasoning that the sum of degrees must be even and at most 4×5=20, yielding x∈{0,2,4}. This is significantly easier than average A-level questions as it requires only recall of definitions and minimal calculation. |
| Spec | 7.02a Graphs: vertices (nodes) and arcs (edges)7.02c Graph terminology: walk, trail, path, cycle, route |
| Answer | Marks |
|---|---|
| 3 | 100 |
| 3 | 100 |
I'd be happy to help clean up mark scheme content, but the text you've provided appears to be incomplete or corrupted. It shows:
```
Question 3:
3 | 100
3 | 100
```
This doesn't contain any actual marking points, unicode symbols to convert, or marking annotations (M1, A1, B1, etc.) to preserve.
Could you please provide the full mark scheme content for Question 3? Once you share the complete text, I'll format it according to your specifications with:
- Unicode symbols converted to LaTeX math notation
- Marking annotations preserved
- Clear formatting with one marking point per line3. (a) Draw a graph with 6 vertices, each of degree 1 .\\
(b) Draw two graphs with 6 vertices, each of degree 2 such that:
\begin{enumerate}[label=(\roman*)]
\item the graph is connected,
\item the graph is not connected.
A simple connected graph has 5 vertices each of degree $x$.\\
(c) Find the possible values of $x$ and explain your answer.\\
(d) For each value of $x$ you found in part (c) draw a possible graph.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 Q3 [7]}}