In this paper , we investigate integral graph as a graph whose spectrum of eigenvalues consists Entirely of integers that was introduced by Harary and Schwenk in 1974. The effect of various binary operations on spectral integral properties is introduced, and several families of such integral graphs are exhibited. The identification of all integral graphs appears to be involved. However , as with many other problems in graph theory , if we restrict our attention to trees, the prospects are much better. Therefore we study trees, specifically integral starlike tree homeomorphic with K_(1,m) and a double starlike tree with order m+n consisting of a vertex of degree m+1 , a vertex of degree n+1, and all other vertices having degree 1. Finally in determining a double starlike tree is integral , we reach the following equation: (A^2-1)(B^2 -1)=C^2 Which R.Graham, in 1980, proved that all solutions are just given by the value of Chebyshev polynomials evaluated at integers.

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