**ABSTRACT**

A (p, q) graph G is said to admit higher order triangular graceful labeling if its vertices can be labeled by the integers from 0 to q^{th} higher order triangular numbers such that the induced edge labels obtained by the absolute difference of the labels of end vertices are the first q higher order triangular numbers. A graph G which admits higher order triangular graceful labeling is called a higher order triangular graceful graph. In this paper, third order, fourth order, fifth order triangular graceful labeling are introduced and third order, fourth order, fifth order triangular graceful labeling of star graph, subdivision of star, nK2 path, comb, bistar, coconut tree, nK1,3 are studied.

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