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Open Access Research Article

On enumeration of labeled connected transitive digraphs

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pp. 1329–1340Vol. 26Issue 6September 2023DOI: 10.47974/JIM-1631XML
Published Online:
08 Sep 2023
Article type:
Research Article
Language:
EN
Article no.:
JIM-1631
Pages:
1329–1340

Abstract

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. 

Keywords

Subject Classifications

(2020) 05C30

Acknowledgements

FRH-P936H86

References

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