Year: 2025
Type: article
Abstract: Let D be a digraph, a subset S of V(D) is called in-dominating set in D if for each vertex x ∈ V(D) S there is a vertex w ∈ S such that (x, w) ∈ A(D). An in-domatic partition of D is a partition of V(D) where all parts are in-dominating sets in D. The maximum number of parts of an in-domatic partition of D is the in-domatic number of D and it is denoted by d⁻(D). In this work, the in-domatic number for some families of digraphs such as complete digraphs, transitive digraphs, directed cycles and the cartesian product of two cycles, is calculated. Also, in-domatically critical digraphs are characterized. Additionally, the in-domatic partitions of the line digraph and some other operations which reflect the adjacency and incidence relations in digraphs are explored.
Institution: Universidad Nacional Autónoma de México
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G8208106529
OpenAlex ID: W7126299231
FWCI:
Cites:
Cited by:
Related to: