Embedding Trees Gracefully on the Triangular Grids

As today, after almost 35 years the famous Graceful Trees Conjecture (GTC), remains widely open. Several unsuccessful methods have been devised in the past to settle this tree labeling conjecture. In this paper we re-formulated it as a tree embeding problem and show the equivalance of embedding trees with at most vertex degree three onto the triangular grids with some specific properties with the orginal graceful tree labeling