| Title: | In-domatic number and some operations in digraphs |
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| Authors: | ID Benítez-Bobadilla, Germán (Author)
ID Pastrana-Ramírez, Laura (Author) |
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| Files: |  AMC_Benitez-Bobadilla,_Pastrana-Ramirez_2026.pdf (420,14 KB)
MD5: 3C61EB57B41DFA069E23A97262AB3F6A
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| 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. |
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| Keywords: | in-domatic number, in-domatically critical digraph, line digraph, in-domatically full digraph, cartesian product |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 10.11.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 16 str. |
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| Numbering: | Vol. 26, no. 1, [article no.] P1.02 |
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| PID: | 20.500.12556/RUP-22286  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.2988.2bf |
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| Publication date in RUP: | 21.12.2025 |
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| Views: | 190 |
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| Downloads: | 2 |
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