Quasi-amply-regularity and Generalized Hamming Graphs

Let Gλ be the class of the amply-regular graphs with parameters (n,k,λ,2) and Gλ1,λ2 be the one of the quasi-amply-regular graphs with parameters (n,k,λ1,λ2,2). We first give some particular properties of G1 with new proofs and a new characterization of the Hamming graphs H(d, 3). Then under some conditions, we provides a characterization of the generalized Hamming graphs H(d1,λ1+2;d2,λ2+2) obtained by a cartesian product of H(d1,λ1+2) and H(d2,λ2+2) as a quasi-amply-regular graphs with parameters (n,k,λ1,λ2,2) of maximum order for a given degree.