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Constant Sum Partition of Sets of Integers and Distance Magic Graphs

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Cichacz S., Gőrlich A.

Discussiones Mathematicae Graph Theory

2017

tom 38

nr 1

97-106

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Cichacz S.

1 Gőrlich A.

1 2018

Wyniki wyszukiwania

Constant Sum Partition of Sets of Integers and Distance Magic Graphs