# Constant Sum Partition of Sets of Integers and Distance Magic Graphs

• Volume: 38, Issue: 1, page 97-106
• ISSN: 2083-5892

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## Abstract

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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 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.

## How to cite

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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 -

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