Graceful valuations of 2-regular graphs with two components Original Research Article

The following condition (due to A. Rosa) is known to be necessary for a 2-regular graph G to have a graceful valuation: ∥E(G)∥  0 or 3 (mod 4). The condition is also sufficient if G is a cycle. In 1984, A. Kotzig published without proof a theorem stating that this condition is sufficient also for 2-regular graphs with two components. The purpose of this paper is to show that this theorem is valid and also that Rosaʹs condition is not sufficient (without additional assumptions) for 2-regular graphs with more than two components