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 A1, A2, . . . , At, B1, B2, . . . , Bt such that |Ai| = m and |Bi| = n, and ∑a∈Ai a = ∑b∈Bj 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.
@article{bwmeta1.element.doi-10_7151_dmgt_1991,
author = {Sylwia Cichacz and Agnieszka G\H orlich},
title = {Constant Sum Partition of Sets of Integers and Distance Magic Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {38},
year = {2018},
pages = {97-106},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1991}
}
Sylwia Cichacz; Agnieszka Gőrlich. Constant Sum Partition of Sets of Integers and Distance Magic Graphs. Discussiones Mathematicae Graph Theory, Tome 38 (2018) pp. 97-106. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1991/