Authors:
S. Cichacz, A. G§rlich
Title:
Constant sum partition of sets of integers and distance magic graphs
Source:
Discussiones Mathematicae Graph Theory
Received 25.02.2016, Revised 07.10.2016, Accepted 08.10.2016, doi: 10.7151/dmgt.1991

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∈Aia=∑b∈Bjb 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.
Keywords:
constant sum partition, distance magic labeling, product of graphs

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