Year: 2025
Type: article
Abstract: Let 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 φψ from V(G⃗) to Γ by φψ(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 [8]. 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.
Source: Ars Mathematica Contemporanea
Author: Sylwia Cichacz
Institution: AGH University of Krakow
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410901207