Geodesic
Union of Distance Magic Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 239-249

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A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection 𝓁 from V to the set 1, . . ., n such that the weight w(x) = Σ_ y ∈ N_G (x) 𝓁(y) of every vertex x ∈ V is equal to the same element μ, called the magic constant. In this paper, we study unions of distance magic graphs as well as some properties of such graphs.
Keywords: distance magic labeling, magic constant, sigma labeling, graph labeling, union of graphs, lexicographic product, direct product, Kronecker product, Kotzig array 
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Cichacz, Sylwia; Nikodem, Mateusz. Union of Distance Magic Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 239-249. http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a16/