Authors: S. Cichacz, A. Gõrlich 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 A^{1},A^{2},..., A^{t},B^{1},B^{2},...,B^{t} such that |A^{i}|=m and |B^{i}|=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. | |
Keywords: constant sum partition, distance magic labeling, product of graphs | |
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