graph theory – Covering edge in a DAG

The book from which I am studying graph theory has this definition of a covering edge:

If $a$ and $b$ are distinct nodes of a digraph, then $a$ is said to cover $b$ if there is an
edge from $a$ to $b$ and every path from $a$ to $b$ includes this edge. If $a$ covers $b$, the
edge from $a$ to $b$ is called a covering edge.

From what I understand from this definition, $a$ is said to cover $b$ if:

  • There is an edge from $a$ to $b$
  • There is only $1$ path from $a$ to $b$. (Since any other path from $a$ to $b$ would not traverse this edge.)

If I am right, then the covering edges of this DAG would be {($1$,$2$),($1$,$3$),($1$,$5$),($2$,$4$),($2$,$6$),($3$,$6$)}.

Am I correct? If not, then what should be the covering edges in this digraph?