Highly Influenced

8 Excerpts

- Published 2013 in Australasian J. Combinatorics

Let G = (V,E) be a graph and Γ an abelian group, both of order n. A group distance magic labeling of G is a bijection : V → Γ for which there exists μ ∈ Γ such that ∑x∈N(v) (x) = μ for all v ∈ V, where N(v) is the neighborhood of v. Froncek [Australas. J. Combin. 55 (2013), 167–174] showed that the cartesian product Cm Cn, m,n ≥ 3 is a Zmn-distance magic graph if and only if mn is even. In this paper we show some Γdistance magic labelings for Cm Cn where Γ ∼= Zmn. Moreover we will deal with group distance labeling of the pth power of a cycle Cn.

@article{CichaczPrzenioslo2013GroupDM,
title={Group distance magic labeling of some cycle-related graphs},
author={Sylwia Cichacz-Przenioslo},
journal={Australasian J. Combinatorics},
year={2013},
volume={57},
pages={235-244}
}