Irregular graph labelings in Abelian groupsCichacz, Sylwia (Avtor) finite Abelian groupdirected graphzero-sum setsLet G⃗ = (V,E) be a directed graph of order n. If there exists a mapping ψ from E(G⃗) to an Abelian group Γ such that if we define a mapping φ_ψ from V(G⃗) to Γ by φ_ψ(x) = ∑y ∈ N⁺(x)ψ(xy) − ∑y ∈ N⁻(x)ψ(yx),   (x ∈ V(G⃗)), then φψ is injective, then such a labeling ψ is called Γ-irregular. Recently it was showed that if n is large enough then G⃗ has a Γ-irregular labeling for any Γ such that |Γ| > (1 + ε)n (in the paper from Cichacz and Tuza from 2022). In this paper, we prove that if all weakly connected components of G⃗ are of size at least 4, then G⃗ has a Γ-irregular labeling for any finite group Γ such that |Γ| >= n + 5. Založba Univerze na Primorskem20262026-08-11 11:23:07Članek v reviji23441UDK: 51eISSN: 1855-3974DOI: 10.26493/1855-3974.3380.cb8sl