Hamming graph is known to be an important class of graphs, and
it is a challenge to obtain algorithms that recognize whether a given graph G
is a Hamming graph. let R be a commutative  graded ring and S be the set of homogeneous elements.

The Cayley graph Cay(R,S) is a graph whose vertex set is R and two vertices a and b are adjacent if and only if a−b ∈ S. We show that any Hamming graph over sets of prime power sizes is isomorphic to Cay(R, S′) for some graded ring R and a subset S′ of  S