20.500.12556/RUP-22286 In-domatic number and some operations in digraphs Vhodno dominacijsko število in nekatere operacije v usmerjenih grafih 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. in-domatic number in-domatically critical digraph line digraph in-domatically full digraph cartesian product vhodno dominacijsko število vhodno dominacijsko kritičen digraf povezavni digraf vhodno dominacijski polni digraf kartezični produkt true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-12-21 22:06:41 2025-12-21 22:06:42 2026-01-05 11:58:52 0000-00-00 00:00:00 2026 0 0 16 str. no. 1, [article no.] P1.02 Vol. 26 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-11-10 51 1855-3974 10.26493/1855-3974.2988.2bf AMC_Benitez-Bobadilla,_Pastrana-Ramirez_2026.pdf AMC_Benitez-Bobadilla,_Pastrana-Ramirez_2026.pdf 1 3C61EB57B41DFA069E23A97262AB3F6A e9c48d02e015125666e34d763ccdaa98b20895bb62ce9a49e8c151ea4a4cc03f 03dc6904-deb2-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32367 Založba Univerze na Primorskem 0 0 0