Orientable Z_n-distance magic regular graphs [article]

Karolina Szopa, Paweł Dyrlaga
<span title="2018-12-27">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Hefetz, Mütze, and Schwartz conjectured that every connected undirected graph admits an antimagic orientation. In this paper we support the analogous question for distance magic labeling. Let Γ be an Abelian group of order n. A directed Γ-distance magic labeling of an oriented graph G⃗ = (V,A) of order n is a bijection l⃗:V →Γ with the property that there is a magic constant μ∈Γ such that for every x ∈ V(G) w(x) = ∑_y ∈ N^+(x)l⃗(y) - ∑_y ∈ N^-(x)l⃗(y) = μ. In this paper we provide an infinite
more &raquo; ... mily of odd regular graphs possessing an orientable Z_n-distance magic labeling. Our results refer to lexicographic product of graphs. We also present a family of odd regular graphs that are not orientable Z_n-distance magic.
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