On triangular graceful graphs

A labeling or valuation of a graph G is an assignment of labels to the vertices of G that induces for each edge xy a label depending on the vertex labels φ(x) and φ(y). The assignment is said to be triangular graceful if the induced edge values are of the form (T₁,T₂,…,T_n) which are obtained by | φ(x)- φ(y)| where T_n is the n^th triangular number and n is the number of edges. In this paper we study some classes of triangular graceful graphs.