CONSTANT SUM PARTITION OF SETS OF INTEGERS AND DISTANCE MAGIC GRAPHS

Let A = {1, 2,..., t(m)+t(n)}. 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 vertical bar A(i)vertical bar = m and vertical bar B-i vertical bar = n, and Sigma(a is an element of Ai) a = Sigma(b is an element of 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.