Strong in-domatic number in digraphs
Laura Pastrana-Ram\'irez, Roc\'io S\'anchez-L\'opez, Miguel, Tecpa-Galv\'an

TL;DR
This paper introduces the concept of strong in-domatic number in digraphs, explores its properties in various classes of digraphs, and examines how it behaves under different graph operations and modifications.
Contribution
It defines the strong in-domatic number, determines its values for specific digraph classes, and studies its structural properties and behavior under graph operations.
Findings
Determined the strong in-domatic number for semicomplete and planar digraphs.
Identified structural properties and bounds for the strong in-domatic number.
Characterized strong in-domatic critical digraphs and provided specific families.
Abstract
Let be a digraph and a partition of . We say that is a strong in-domatic partition if every in holds that every vertex not in has at least one out-neighbor in , that is is an in-dominating set, and is strongly connected. The maximum number of elements in a strong in-domatic partition is called the strong in-domatic number of and it is denoted by . In this paper we introduce those concepts and determine the value of 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 . Then we study this concept in the Cartesian product, composition, line digraph and other associated digraphs. In addition, we characterize strong…
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Graph theory and applications
