Geodesic
Constant Sum Partition of Sets of Integers and Distance Magic Graphs
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 97-106

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Let A = 1, 2, . . ., tm+tn. We shall say that A has the (m, n, t)-balanced constant-sum-partition property ((m, n, t)-BCSP-property) if there exists a partition of A into 2t pairwise disjoint subsets A^1, A^2, ... , A^t, B^1, B^2, ... , B^t such that | A^i | = m and | B^i | = n, and Σ_ a ∈ A^i a = Σ_ b ∈ B^j b for 1 ≤ i ≤ t and 1 ≤ j ≤ t. In this paper we give sufficient and necessary conditions for a set A to have the (m, n, t)-BCSP-property in the case when m and n are both even. We use this result to show some families of distance magic graphs.
Keywords: constant sum partition, distance magic labeling, product of graphs 
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     title = {Constant {Sum} {Partition} of {Sets} of {Integers} and {Distance} {Magic} {Graphs}},
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Cichacz, Sylwia; Gőrlich, Agnieszka. Constant Sum Partition of Sets of Integers and Distance Magic Graphs. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 97-106. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a7/