21M.1.AHL.TZ1.16

pestleMathematicsAIHLPaper 121M· ahl-3-15-adjacency-matrices-and-tablessource ↗

An ant is walking along the edges of a wire frame in the shape of a triangular prism.

The vertices and edges of this frame can be represented by the graph below.

Write down the adjacency matrix, $M$ , for this graph.

[3]

Find the number of ways that the ant can start at the vertex $A$ , and walk along exactly $6$ edges to return to $A$ .

[2]

Markscheme / solution

$M = (\begin{matrix} 0 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 & 1 & 1 \\ 0 & 1 & 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 & 1 & 0 \end{matrix})$ A1A1A1

Note: Award A1 for each two correct rows.

[3 marks]

calculating $M^{6}$ (M1)

$143$ A1

[2 marks]

Examiners’ report

[N/A]