Hamming polynomials and their partial derivatives

International audienceHamming graphs are Cartesian products of complete graphs and partial Hamming graphs are their isometric subgraphs. The Hamming polynomial h(G) of a graph G is introduced as the Hamming subgraphs counting polynomial. Kk -derivates of a partial Hamming graph are also introduced. It is proved that for a partial Hamming graph G, the derivate of its polynomial is the polynomial of its derivate. A couple of combinatorial identities involving the coefficients of the Hamming polynomials of Hamming graphs are also proven