THE LINE GRAPH MODEL - PREDICTING PHYSICOCHEMICAL PROPERTIES OF ALKANES

For a molecular graph G we construct a sequence of graphs L-i(G), i = 0, 1, 2,..., such that L-0(G) = G, L-1(G) is the line graph of G, L-2( G) is the line graph of L-1(G), etc. Let theta(i) be the value of some topological index TI, associated with L-i(G). We examine the possibil ity to model the structural dependency of certain physico-chemical pro perties of alkanes (boiling point, molar volume, molar refraction, hea t of vaporization, critical temperature, critical pressure and surface tension) by means of linear functions of the parameters theta(i), i = 0, 1,..., k. It is shown that the use of line graphs and, in some cas es, of the second line graphs, results in a significant improvement in the predictive power of topological indices. The line graphs with i g reater than or equal to 3 seem to play a negligible role. In the prese nt work the choices for TI with theta(i) = number of vertices of L-i(G ) and theta(j) = Wiener index of L-j(G) are pursued.