Collection of Czechoslovak Chemical Communications - digital archive 

Abstract

The relation between the Rouse matrix R and the Zimm matrix Z, defined for polymer chains, is generalized for all trees. The path matrix W_u of an unoriented tree and the walk matrix W_o of an oriented tree are defined and their relations with the corresponding incidence matrices G and S of trees: (GG^T) = n(W_u^TW_u)^-1 and (SS^T) = n(W_o^TW_o)^-1 are proved. The elements of the quadratical forms W^TW are the number of path (selfavoiding walks) in which the edge (arc) i is present together with the edge (arc) j. The traces of W^TW are the Wiener path number.