Polychrome labelings of trees and cycles

This paper deals with a new kind of graph labeling similar to the well known harmonious, graceful, and elegant labelings. A polychrome labeling of a simple and connected graph G = (V, E) by an abelian group A is a bijective map from V onto A such that the induced edge labeling f*(vw) = f(v)+f(w), vw epsilon E, is injective. Polychrome labelings of a path and a cycle by a large class of abelian groups are designed, and the connection to the above mentioned labelings is shown. in addition, the author presents a conjecture which is similar to a famous conjecture of G. Ringel about graceful trees (see. [9]).