Sách A q-analogue of Graham, Hoffman and Hosoya’s Theorem

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