The Four Connectivity Matrices, Their Indices, Polynomials and Spectra

The four connectivity matrices are presented: the vertex-product-connectivity matrix, the edge-product-connectivity matrix, the vertex-sum-connectivity matrix and the edge-sum-connectivity matrix. The half-sum of their matrix elements are the corresponding connectivity indices: the vertex-product-connectivity index, the edgeproduct- connectivity index, vertex-sum-connectivity index and the edge-sumconnectivity index. The suitability of these four forms of connectivity indices in developing structure-property relationships is illustrated on four sets of alkanes for 14 experimental physico-chemical properties. Their polynomials and spectra are also given. The method used for constructing polynomials of the connectivity matrices considered is the Le Verrier-Fadeev-Frame method, that has been modified by Balasubramanian and Živković.

Keywords: Connectivity matrix, connectivity index, vertex-product, edgeproduct, vertex-sum, edge-sum, connectivity matrix spectra, connectivity matrix polynomial, matrix polynomial computation, Le Verrier-Fadeev-Frame method, structure-property relationship, inter-correlation, comparative correlational analysis, alkane data sets, branched alkanes, non-branched alkanes, physicochemical properties, boiling points, melting points, vaporization enthalpy, standard Gibbs energy of formation, refractive index, density, molar heat capacity.