DISTANCE DISTANCE MATRICES

We introduce novel matrices for graphs embedded on two- and three-dimensional grids. The matrices are defined in terms of geometrical and topological distances in such graphs. We report on some properties of these distance/distance matrices and have listed several structural invariants derived from distance/distance matrices. The normalized Perron root (the first eigenvalue) of such matrices, lambda/n, for path graphs apparently is an index of molecular folding. The ratio phi = lambda/n is 1 for (geometrically) linear structures, while it approaches 0 as the path graph is repeatedly folded.