2.6 Directed Acyclic Graphs (DAGs) & Scheduling

DAGs

Which of the following graph features may NOT appear in a digraph:

Exercise 1
  self loops

  isolated nodes (with no edges in or out)

  two edges in opposite directions between a pair of nodes

  two edges in the same direction between a pair of nodes

  having no edges at all

  having no nodes at all

Let \(V\) be a DAG and \(U\) be the DAG with only the covering edges of \(V\). Then,
1. compared to the length of the shortest path between two nodes in \(V\), the length of the shortest path in \(U\) between these nodes is:
  
  Exercise 2
    not shorter
2. compared to the length of the longest path between two nodes in \(V\), the length of the longest path in \(U\) between these nodes is:
  
  Exercise 3
    the same