Every labeling of the vertices of a graph with distinct natural number
s induces a natural labeling of its edges: the label of an edge (x, y)
is the absolute value of the difference of the labels of x and y. By
analogy with graceful labelings, we say that a labeling of the vertice
s of a graph of order n is minimally k-equitable if the vertices are l
abeled with 1,2,..., n and in the induced labeling of its edges every
label either occurs exactly k times or does not occur at all. Bloom [3
] posed the following question: Is the condition that k is a proper di
visor of n sufficient for the cycle C(n) to have a minimal k-equitable
labeling? We give a positive answer to this question. (C) 1993 John W
iley & Sons, Inc.