Constructing Trees with Graceful Labelings Using Caterpillars

Hrnciar and Haviar [3] gave a method to construct a graceful labeling for all trees of diameter at most five. Based on their method and the methods described in Balbuena et al. [1], we shall describe a new construction for gracefully labeled trees by attaching trees to the vertices of a tree admitting a bipartite graceful labeling.