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.
