On enumeration of labeled connected transitive digraphs
Kh. Sh. Al’Dzhabri, В.И. Родионов · Journal of Interdisciplinary Mathematics · 2023
If Tc0(n) is the number of all labeled connected transitive digraphs defined on a set of n elements, then the formula Tc0(n) = S pˉ = (p1, ..., pk)| = n (-1)n-k (np) W c (pˉ) is true. The summation is over all sequences pˉ= (p1, ..., pk) ∈ ℕk1 such that p1 +...+ pk = n. Term W c (pˉ) denotes the number of labeled connected transitive digraphs of a special form, depending on the parameter pˉ.