Adjacency matrices Problem set B Answers

\(\begin{pmatrix}2 & 1 & 2 & 0 \\ 1 & 0 & 1 & 1 \\ 2 & 1 & 0 & 1 \\ 0 & 1 & 1 & 0\end{pmatrix}\)

1. (a) Edges: a loop at P, PQ, PS, QR (2 edges) and RS
2. (b) 6

1. (a) Q and S
2. (b) 4

1. (a) 1
2. (b) 2
3. (c) 7

1. (a) Edges: P to R, P to S, Q to P, Q to R, S to Q and S to R
2. (b) R, with in-degree 3

1. (a) \(\begin{pmatrix}0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 & 0\end{pmatrix}\)
2. (b) S, out-degree 3
3. (c) Q, in-degree 3

1. (a) W, Y and Z
2. (b) 5
3. (c) X, degree 4

1. (a) X, 6 parcels
2. (b) Z, 5 parcels
3. (c) 13

1. (a) x = 4
2. (b) 8

1. (a) x = 3
2. (b) y = 3