Moderate -0.8 This is a straightforward recall and application question requiring students to check vertex degrees (for Eulerian/semi-Eulerian) and identify a Hamiltonian cycle in a small 5-vertex graph. Both are standard definitions with mechanical checking procedures, making this easier than average despite being Further Maths content.
2 The graph \(G\) has 5 vertices and 6 edges, as shown below.
\includegraphics[max width=\textwidth, alt={}, center]{21ed3b4e-a089-4607-b5d6-69d8aac03f31-03_547_547_360_749}
Which of the following statements describes the properties of \(G\) ?
Tick ( \(\checkmark\) ) one box.
\(G\) is Eulerian and Hamiltonian. □
\(G\) is Eulerian but not Hamiltonian. □
\(G\) is semi-Eulerian and Hamiltonian. □
\(G\) is semi-Eulerian but not Hamiltonian. □
2 The graph $G$ has 5 vertices and 6 edges, as shown below.\\
\includegraphics[max width=\textwidth, alt={}, center]{21ed3b4e-a089-4607-b5d6-69d8aac03f31-03_547_547_360_749}
Which of the following statements describes the properties of $G$ ?\\
Tick ( $\checkmark$ ) one box.\\
$G$ is Eulerian and Hamiltonian. □\\
$G$ is Eulerian but not Hamiltonian. □\\
$G$ is semi-Eulerian and Hamiltonian. □\\
$G$ is semi-Eulerian but not Hamiltonian. □
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2020 Q2 [1]}}