Year: 2025
Type: article
Abstract: Let G(V, E) be a graph, where V and E are the vertex set and edge set, respectively.A local antimagic labelling of G is a bijection f : E → {1, 2, . . ., |E|} such that for every edge uv ∈ E, the condition e∈I(u) f (e) ̸ = e∈I(v) f (e) holds, where I(u) represents the set of edges incident to u. Bensmail, Senhaji, and Lyngsie [Discrete Math.Theor.Comput.Sci.19 (2017) #21] proposed a recursive algorithm for local antimagic labelling of trees.In this article, we propose a linear-time iterative algorithm for computing a local antimagic labelling for trees.A major tool used in this algorithm is a specific partitioning scheme, introduced by Kaplan, Lev, and Roditty [Discrete Math.309 (2009) 2010-2014].We believe that our technique can be generalised to achieve local antimagic labelling for some superclasses of trees.
Source: Contributions to Mathematics
DOI: 10.47443/cm.2025.013
Authors: Subhabrata Paul, Soumen Raul
Institution: Indian Institute of Technology Patna
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: University Grants Commission
OpenAlex ID: W4409438829