Adjacency matrices Problem set A Answers

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

1. (a) Edges: AB (2 edges), AD, BC, a loop at C and CD
2. (b) 6

1. (a) A, D and E
2. (b) 4

1. (a) 2
2. (b) 1
3. (c) 6

1. (a) Edges: A to B, A to C, B to C, C to A and D to C
2. (b) C, with in-degree 3

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

1. (a) P, R and S
2. (b) 5
3. (c) Q, degree 4

1. (a) A, 4 messages
2. (b) B, 5 messages
3. (c) 11

1. (a) x = 3
2. (b) 7

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