2 A simply connected semi-Eulerian graph G has 6 vertices and 8 arcs. Two of the vertex degrees are 3 and 4.
- Determine the minimum possible vertex degree.
- Determine the maximum possible vertex degree.
- Write down the two possible degree sequences (ordered lists of vertex degrees).
The adjacency matrix for a digraph H is given below.
| \multirow{7}{*}{From} | \multirow{2}{*}{} | To |
| | J | K | L | M | N |
| J | 0 | 1 | 1 | 0 | 0 |
| K | 1 | 0 | 1 | 0 | 0 |
| L | 1 | 0 | 0 | 0 | 1 |
| M | 0 | 0 | 2 | 1 | 1 |
| N | 0 | 1 | 0 | 1 | 0 |
- Write down the indegree and the outdegree of each vertex of H .
- Use the indegrees and outdegrees to determine whether graph H is Eulerian.
- Use the adjacency matrix to determine whether graph H is simply connected.