24.1.1. Introduction to In Degrees

Try these first

1. 1.

   What is the in degree of a vertex?

   Hint

   Think about incoming arrows in a directed graph.

2. 2.

   If a vertex has no incoming edges, what is its in degree?

   Hint

   Consider what it means to have no connections coming in.

3. 3.

   What does an in degree of 0 indicate about a vertex?

   • It has no outgoing edges
   • It has no incoming edges
   • It cannot be removed

   Hint

   Think about what it means in the context of task dependencies.

4. 4.

   True or False: Topological sorting can produce multiple valid orderings.

   • True
   • False

   Hint

   Consider scenarios with branches in task dependencies.

5. 5.

   You are given a DAG representing tasks and their dependencies. Vertex 'A' has edges leading to 'B', 'C', and 'D'. If 'A' is removed, what will be the in degrees of 'B', 'C', and 'D'?

   Hint

   Count how each vertex is affected by the removal of 'A'.

6. 6.

   Demonstrate how the choice of vertices with in degree 0 affects the resulting topological order in a DAG you create.

   Hint

   Draw the graph and label the in degrees before experimenting!