Constant Sum Partition of Sets of Integers and Distance Magic Graphs

Sylwia Cichacz, and Agnieszka Gőrlich. "Constant Sum Partition of Sets of Integers and Distance Magic Graphs." Discussiones Mathematicae Graph Theory 38.1 (2018): 97-106. <http://eudml.org/doc/288353>.

@article{SylwiaCichacz2018,
abstract = {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.},
author = {Sylwia Cichacz, Agnieszka Gőrlich},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {constant sum partition; distance magic labeling; product of graphs},
language = {eng},
number = {1},
pages = {97-106},
title = {Constant Sum Partition of Sets of Integers and Distance Magic Graphs},
url = {http://eudml.org/doc/288353},
volume = {38},
year = {2018},
}

TY - JOUR
AU - Sylwia Cichacz
AU - Agnieszka Gőrlich
TI - Constant Sum Partition of Sets of Integers and Distance Magic Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2018
VL - 38
IS - 1
SP - 97
EP - 106
AB - 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.
LA - eng
KW - constant sum partition; distance magic labeling; product of graphs
UR - http://eudml.org/doc/288353
ER -