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

Sylwia Cichacz; Agnieszka Gőrlich

Discussiones Mathematicae Graph Theory (2018)

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

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topSylwia 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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