(a)
Attempt to create a 5×5 adjacency matrix
\[ M = \begin{pmatrix} 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \end{pmatrix} \]
Result: \( M = \begin{pmatrix} 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \end{pmatrix} \) [3]

(b)(i)
Recognizing need to find \( M^7 \)
\[ M^7 = \begin{pmatrix} 8 & 8 & 17 & 8 & 13 \\ 8 & 10 & 19 & 17 & 14 \\ 6 & 11 & 16 & 10 & 17 \\ 11 & 8 & 19 & 14 & 10 \\ 2 & 6 & 8 & 11 & 8 \end{pmatrix} \]
2 (routes)
Result: 2 routes [2]

(b)(ii)
Vertices visited in order are
EITHER \( E \rightarrow D \rightarrow C \rightarrow B \rightarrow C \rightarrow B \rightarrow D \rightarrow A \)
OR \( E \rightarrow D \rightarrow C \rightarrow B \rightarrow C \rightarrow E \rightarrow D \rightarrow A \)
Result: \( E, D, C, B, C, B, D, A \) [2]