Constant sum partition of sets of integers and distance magic graphs
Sylwia Cichacz, Agnieszka Görlich · Discussiones Mathematicae Graph Theory · 2017
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 aA i a = bB 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.