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On closed distance magic circulants of valency up to 5
Fernández, Blas ...
Let ▫$\Ga=(V,E)$▫ be a graph of order ▫$n$▫. A {\em closed distance magic labeling} of ▫$\Ga$▫ is a bijection ▫$\ell : V \to \{1,2, \ldots, n\}$▫ for which there exists a positive integer ▫$r$▫ such ...that ▫$\sum_{x \in N[u]} \ell(x) = r$▫ for all vertices ▫$u \in V$▫, where ▫$N[u]$▫ is the closed neighborhood of ▫$u$▫. A graph is said to be {\em closed distance magic} if it admits a closed distance magic labeling. In this paper, we classify all connected closed distance magic circulants with valency at most ▫$5$▫, that is, Cayley graphs ▫$\Cay(\mathbb Z_n;S)$▫ where ▫$|S| \le 5$▫, ▫$S = -S$▫, ▫$0 \not\in S$▫ and ▫$S$▫ generates ▫$\mathbb Z_n$▫.
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