Year: 2025
Type: article
Abstract: Let $G=(V,E)$ be a graph with $p$ edges and let $f$ be a bijective function from $E(G)$ to $\{1,2,\dots ,p\}$.For any vertex $v$, let $\phi_f(v)$ denote the sum of $f(e)$ over all edges $e$ incident to $v$.If $\phi_f(v)\not=\phi_f(u)$ holds for any two distinct vertices $u$ and $v$, then $f$ is called an antimagic labelling of $G$.A graph $G$ is deemed antimagic if it admits such a labelling.In this study, we investigate the antimagic properties of graph unions, particularly focusing on structures composed of multiple triangles and 3-paths. We employ Skolem sequences and extended Skolem sequences to construct antimagic labelling for these graph unions. Specifically, we demonstrate that for any integer $n\geq 9$, the graph formed by the disjoint union of $m$ copies of the triangle $C_3$ and $n$ copies of the path $P_3$ is antimagic for $m\geq \lceil\frac{n}{3}\rceil$.
Source: Tamkang Journal of Mathematics
Authors: Chen Voon, Say Sian Tay
Institution: Universiti Tunku Abdul Rahman
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409587424