On constant sum partitions and applications to distance magic-type graphs

Abstract

Let be an additive abelian group of order and let be a partition of where A constant sum partition (or -sum partition) of is a pairwise disjoint union of subsets such that and for some fixed and every In 2009, Kaplan, Lev, and Roditty proved that a 0-sum partition of the cyclic group exists for odd if and only if In this paper, we address the case when is even. In particular, we show that a -sum partition of exists for even and odd if and only if Moreover, we provide applications to distance magic-type graphs including the classification of -distance magic complete -partite graphs for odd.

Keywords

• constant sum partition
• group distance magic graphs
• orientable distance magic graphs