... Lemma 3, we show that qcofsumw is independent of w (and hence can G be denoted as qcofsumG ) In Subsection 3.1, we prove the following q-analogue of Graham, Hoffman and Hosoya’s result Theorem ... cu,v is the sum of the cofactors of qDG Proof: We recall that qDG is the q-analogue of the distance matrix DG = (du,v ) of G and qCOFG = (cu,v ) is the cofactor matrix of qDG For two vertices ... the q-analogue of DG be qDG and let G have blocks G1 , G2 , , Gr For each i r, let the distance matrix of Gi and its q-analogue be DGi and qDGi respectively Then, qcofsumG = r i=1 qcofsumGi...