Transformations of distances into adjacencies

摘要

The code matrix of trees generates their distance matrix, and transforms the incidence matrix of the complete graph into the path matrix. Adjacency and distance matrices of all graphs are related by the transformation distance moments (d_ij)~k as a_ij=lim (d_ij)~k The dependence of the eigenvalues of distance=-moment matrices on k is studied on the examples of a 5-vertex linear chain, a 4-membered cycle and a cube. The distance moments can also be changed by different configurations of molecular graphs. The chemical significance of the results obtained is pointed out.