Group distance magic cubic graphs
Abstract
A $Γ$\emph{-distance magic labeling} of a graph $G = (V, E)$ with $|V| = n$ is a bijection $\ell$ from $V$ to an Abelian group $Γ$ of order $n$, for which there exists $μ\in Γ$, such that the weight $w(x) =\sum_{y\in N(x)}\ell(y)$ of every vertex $x \in V$ is equal to $μ$. In this case, the element $μ$ is called the \emph{magic constant of} $G$. A graph $G$ is called a \emph{group distance magic} if there exists a $Γ$-distance magic labeling of $G$ for every Abelian group $Γ$ of order $n$. In this paper, we focused on cubic $Γ$-distance magic graphs as well as some properties of such graphs.
Fields of Study & Subjects
Graph Labeling and Dimension Problems
Advanced Graph Theory Research
Publication details
- Journal / source
- Discussiones Mathematicae Graph Theory
- Publisher
- University of Zielona Góra, Poland
- Volume
- 46
- Issue
- 2
- Pages
- 465–465
- Publication date
- 1 January 2026
- Language
- EN