Group distance magic cubic graphs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909977167265792 |
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| author | Cichacz, Sylwia Miklavič, Štefko |
| author_facet | Cichacz, Sylwia Miklavič, Štefko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01423 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Group distance magic cubic graphs Cichacz, Sylwia Miklavič, Štefko Combinatorics 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. |
| title | Group distance magic cubic graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.01423 |