2022
DOI: 10.48550/arxiv.2204.01822
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Strong in-domatic number in digraphs

Abstract: Let D = (V, A) be a digraph and S a partition of V (D). We say that S is a strong in-domatic partition if every S in 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 D S 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 d − s (D). In this paper we introduce those concepts and determine the value of d − s for semicomplete digraphs and planar digraphs.… Show more

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