Number the vertices of a given n-vertex tree with the numbers from the set N={1,2,…,n} so that the resulting induce edge labels which is given by the absolute difference of the labels at its end points constitute the distinct integers 1,2,…,n-1. This is basic definition of the well-known graceful tree conjecture (Ringel [1]-Kotzig [2]). Strong version of this problem is to find a graceful labeling of a given n-vertex tree T such that for every three vertices x , y and z with (x,y), (y,z)e T either f(x)<f(y) and f(y)>f(z) or f(x)>f(y) and f(y)<f(z) hold. It was conjectured that this is true for all trees (Cahit [3]). Several people have interested to this problem (includes D. E. Knuth, J.-C Bermond, Y. Caro ) but even for the comets (terminology used by A. Rosa for 2-stars) it is not decided yet for n>25, n=odd whether all comets have strong graceful labeling. Note that graceful labeling of comets have been shown to be graceful in [4]. The strong graceful labeling of the comet with 19 vertices is shown below as an example.