| Title: | Irregular graph labelings in Abelian groups |
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| Authors: | ID Cichacz, Sylwia (Author) |
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| Files: |  AMC_Cichacz_2026.pdf (331,17 KB)
MD5: AC47343FA13DEBC61C1F7A32ED96CA17
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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 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. |
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| Keywords: | finite Abelian group, directed graph, zero-sum sets |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 31.03.2026 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 10 str. |
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| Numbering: | Vol. 26, no. 2, [article no.] P2.09 |
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| PID: | 20.500.12556/RUP-23441  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3380.cb8 |
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| Publication date in RUP: | 11.08.2026 |
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| Views: | 24 |
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| Downloads: | 0 |
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