The Erd\"os-Falconer distance problem on the unit sphere in vector spaces over finite fields

art, Iosevich, Koh and Rudnev (2007) show, using Fourier analysis method, that the finite Erd"os-Falconer distance conjecture holds for subsets of the unit sphere in $\text{mathbbm}{F}_q^d$. In this note, we give a graph theoretic proof of this result.