Moderate -0.8 This is a straightforward 1-mark multiple choice question requiring basic graph theory definitions. Students need only check vertex degrees (all even → Eulerian) or count edges vs vertices for a tree, which are routine checks requiring minimal calculation and no problem-solving insight.
The simple-connected graph \(G\) has the adjacency matrix
$$\begin{array}{c|cccc}
& A & B & C & D \\
\hline
A & 0 & 1 & 1 & 1 \\
B & 1 & 0 & 1 & 0 \\
C & 1 & 1 & 0 & 1 \\
D & 1 & 0 & 1 & 0 \\
\end{array}$$
Which one of the following statements about \(G\) is true?
Tick \((\checkmark)\) one box.
[1 mark]
\(G\) is a tree \(\square\)
\(G\) is complete \(\square\)
\(G\) is Eulerian \(\square\)
\(G\) is planar \(\square\)
The simple-connected graph $G$ has the adjacency matrix
$$\begin{array}{c|cccc}
& A & B & C & D \\
\hline
A & 0 & 1 & 1 & 1 \\
B & 1 & 0 & 1 & 0 \\
C & 1 & 1 & 0 & 1 \\
D & 1 & 0 & 1 & 0 \\
\end{array}$$
Which one of the following statements about $G$ is true?
Tick $(\checkmark)$ one box.
[1 mark]
$G$ is a tree $\square$
$G$ is complete $\square$
$G$ is Eulerian $\square$
$G$ is planar $\square$
\hfill \mbox{\textit{AQA Further Paper 3 Discrete 2024 Q3 [1]}}