On distance magic circulants of valency 6
| Autor: | Miklavič, Štefko, Šparl, Primož |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Published in Discrete Applied Mathematics, Volume 329, 2023, Pages 35-48 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.dam.2022.12.024 |
| Popis: | A graph $\Gamma = (V,E)$ of order $n$ is {\em distance magic} if it admits a bijective labeling $\ell \colon V \to \{1,2, \ldots, n\}$ of its vertices for which there exists a positive integer $\kappa$ such that $\sum_{u \in N(v)} \ell(u) = \kappa$ for all vertices $v \in V$, where $N(v)$ is the neighborhood of $v$. %It is well known that a regular distance magic graph is necessarily of even valency. A {\em circulant} is a graph admitting an automorphism cyclically permuting its vertices. In this paper we study distance magic circulants of valency $6$. We obtain some necessary and some sufficient conditions for a circulant of valency $6$ to be distance magic, thereby finding several infinite families of examples. The combined results of this paper provide a partial classification of all distance magic circulants of valency $6$. In particular, we classify distance magic circulants of valency $6$, whose order is not divisible by $12$. Comment: 19 pages |
| Databáze: | arXiv |
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