# Term for "Directed acyclic graph with exactly one sink and one source"

There's a theorem/lemma that states that a finite directed acyclic graph (DAG) has at least one sink and at least one source. Is there a term for a (finite) DAG with exactly one sink and one source?

(And while you're at it, any good background references for someone whose research just took a left turn into such DAGs?)

• I guess you're talking only about finite directed acyclic graphs? Jun 16 '13 at 3:31
• @Joel: Yes I was only thinking about finite DAGs. Jun 16 '13 at 3:36
• And I guess (please excuse this trivial remark) one needs to say "nonempty" as well, since the empty graph is directed and acyclic, but has no sources or sinks. Jun 16 '13 at 4:11
• Or, "non-empty well-orderable graphs with no infinite directed paths". $\;$
– user5810
Jun 16 '13 at 21:38
• @JDH: A better statement than adding "nonempty" near the beginning would be to add "in each component" at the end. This gives generically a stronger statement than the one OP started with, and covers the $\emptyset$ case as well. Jun 18 '13 at 2:32

In Fully Dynamic Transitive Closure in Plane Dags with One Source and One Sink (1994) by Thore Husfeldt this is called a source-sink graph (or short st-graph) by Definition (1).