On graceful labelings of trees

Abstract

A tree is a connected acyclic graph. A tree of n vertices is said to be graceful if the vertices can be assigned the labels { 0, 1, 2, ..., n - 1} such that the absolute value of the differences in vertex labels between neighboring vertices generate the set consisting distinct values { 1, 2, 3, ..., n - 1}. Ringel-Kotzig conjectured that all trees are graceful. In this paper we give a partial solution of the conjecture by proving that two large subclasses of trees are graceful. © 2011 Springer-Verlag.