Transitive series-parallel digraph

Transitive series-parallel digraph --- транзитивный параллельно-последовательный орграф.

Transitive series-parallel digraphs are recursively defined as:

(1) A digraph on a single node is TSP (transitive series-parallel).

(2) If [math]\displaystyle{ G_{1} = (V_{1},E_{1}) }[/math] and [math]\displaystyle{ G_{2} = (V_{2},E_{2}) }[/math] are TSP digraphs and [math]\displaystyle{ V_{1} \cap V_{2} = \emptyset }[/math], then

(2.1) [math]\displaystyle{ G_{1} \parallel G_{2} = (V_{1} \cup V_{2}, E_{1} \cup E_{2}) }[/math] is a TSP digraph (the parallel composition).

(2.2) [math]\displaystyle{ G_{1} \rightarrow G_{2} = (V_{1} \cup V_{2}, E_{1} \cup E_{2} \cup (V_{1} \times V_{2})) }[/math] is a TSP digraph (the series composition).

(3) There are no further TSP digraphs.