A note on graceful trees.

The binomial acyclic graph B 0 ¯ comprises one node. The binomial acyclic graph Bk- B k ¯ is an ordered tree-defined repertoire. The binomial acyclic graph B k ¯ comprises of two binomial acyclic trees B k − 1 ¯ that are linked together. The root of one is the leftmost child of the root of the other. In this paper, we introduce the power of three acyclic graphs for every r, non-negative integer, and prove that power of three acyclic graphs is graceful labeling and also show that every binomial and power of three acyclic graphs is cube sum labeling. [ABSTRACT FROM AUTHOR]