AbstractGraham, Hoffman and Hosoya gave a very nice formula about the determinant of thedistance matrix DG of a graph G in terms of the distance matrix of its blocks. We generalizethis result to a q-analogue of DG. Our generalization yields results about the equality ofthe determinant of the mod-2 (and in general mod-k) distance matrix (i.e. each entry of thedistance matrix is taken modulo 2 or k) of some graphs. The mod-2 case can be interpretedas a determinant equality result for the adjacency matrix of some graphs...