[Graph Theory]

1. A weak component of a digraph is a maximal weakly connected generated subgraph, that is, a weakly connected generated subgraph with the property that if we add any vertices, the subgraph generatd is not weakly connected. Find all weak components of the digraph D_9. Do the same for each digraph of Fig 2.17.

2. Using the definition in the previous exercise, show that every vertex of D is in exactly one weak component.

u w D, dy u w D, dy