New topological matrices and their polynomials

Abstract

New polynomials and molecular graph spectra are derived on the basis of recently proposed matrices, D_A, D_P, and RD_P, and of the previously defined RD_e (reciprocal distance) matrix. The new molecular graph descriptors are exemplified on a collection of path-graphs L_2-L₅ and cyclic-graphs C_3-C₃&bull;. 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(RD_e) and SumCh(RD_p) can be viewed as global descriptors (i.e. topological indices), by analogy with the Hosoya's number <em>Z</em>. Values of the two indices as well as the minimum, MinSp(M), and maximum,&nbsp; 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 good results in modeling the properties of alkanes.