# 2.6 Directed Acyclic Graphs (DAGs) & Scheduling

## The Divisibility DAG

In the above DAG for the divisibility relation on $$\{1, \ldots, 12\}$$, there is an upward path from $$a$$ to $$b$$ iff $$a$$ divides $$b$$. If $$24$$ was added as a vertex, what is the minimum number of edges that must be added to the DAG to represent divisibility on $$\{1, \ldots, 12, 24\}$$?

Exercise 1
Edges from 8 and 12 to 24 are all that are needed.