New topological matrices and their polynomials

New polynomials and molecular graph spectra are derived on the basis of recently proposed matrices, D-Delta, D-P and RDp, and of the previously defined RDe (reciprocal distance) matrix. The new molecular graph descriptors are exemplified on a collection of path-graphs L-2-L-8 and cyclic-graphs C-3-C-8. The polynomials for the last two matrices (both based on a reciprocal relationship) are the first defined polynomials with non-integer coefficients. The sum of their absolute values, denoted as SumCh(RDe) and SumCh(RDp) can be viewed as global descriptors (i.e. topological indices), by analogy with the Hosoya's number Z. Values of the two indices as well as the minimum, MinSp(M), and maximum, MaxSp(M), eigenvalues are listed for nonane isomers. The new structural descriptors have been tested for correlation with some physico-chemical properties and are found to give goad results in modeling the properties of alkanes.