Characterization of Completely $k$-Magic Regular Graphs

@article{Eniego2016CharacterizationOC,
  title={Characterization of Completely \$k\$-Magic Regular Graphs},
  author={Arnold A. Eniego and I. Garces},
  journal={arXiv: Combinatorics},
  year={2016}
}
Let $k \in \mathbb{N}$ and $c \in \mathbb{Z}_k$, where $\mathbb{Z}_1=\mathbb{Z}$. A graph $G=(V(G),E(G))$ is said to be $c$-sum $k$-magic if there is a labeling $\ell:E(G) \rightarrow \mathbb{Z}_k \setminus \{0\}$ such that $\sum_{u \in N(v)} \ell(uv) \equiv c \pmod{k}$ for every vertex $v$ of $G$, where $N(v)$ is the neighborhood of $v$ in $G$. We say that $G$ is completely $k$-magic whenever it is $c$-sum $k$-magic for every $c \in \mathbb{Z}_k$. In this paper, we characterize all completely… Expand
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