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- W4320341817 abstract "Let $D=(V,A)$ be a digraph and $mathfrak{S}$ a partition of $V(D)$. We say that $mathfrak{S}$ is a strong in-domatic partition if every $S$ in $mathfrak{S}$ holds that every vertex not in $S$ has at least one out-neighbor in $S$, that is $S$ is an in-dominating set, and $Dlangle S rangle$ is strongly connected. The maximum number of elements in a strong in-domatic partition is called the strong in-domatic number of $D$ and it is denoted by $mathsf{d}_{s}^{-}(D)$. In this paper we introduce those concepts and determine the value of $mathsf{d}_{s}^{-}$ for semicomplete digraphs and planar digraphs. We show some structural properties of digraphs which have a strong in-domatic partition and we see some bounds for $mathsf{d}_{s}^{-}(D)$. Then we study this concept in the Cartesian product, composition, line digraph and other associated digraphs. In addition, we characterize strong in-domatic critical digraphs and we give two families strong in-domatic critical digraphs which hold some properties, where a strong in-domatic critical digraph $D$ holds that $mathsf{d}_{s}^{-}(D-e) = mathsf{d}_{s}^{-}(D) -1 $ for every $e$ in $A(D)$." @default.
- W4320341817 created "2023-02-13" @default.
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- W4320341817 date "2022-04-04" @default.
- W4320341817 modified "2023-09-27" @default.
- W4320341817 title "Strong in-domatic number in digraphs" @default.
- W4320341817 doi "https://doi.org/10.48550/arxiv.2204.01822" @default.
- W4320341817 hasPublicationYear "2022" @default.
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