Modeling boiling points of cycloalkanes by means of iterated line graph sequences.

A class of models for predicting boiling points of cycloalkanes is put forward, based on iterated line graphs L(i), i = 1, 2,., of the molecular graph G = L(0). Let m(i) be the number of edges of L(i), i = 0, 1, 2,. The models analyzed are of the form a(0)m(i)()(0) + a(1)m(i)(1) + a(2)m(i)(2) +. + a(k)m(ik) + b. Our optimal QSPR formulas contain m(0), m(1), m(2), m(3), and/or m(4) but never m(5) and m(6). Their precision is as good as or better than the approximations recently reported by Rücker and Rücker (J. Chem. Inf. Comput. Sci. 1999, 39, 788-802).

The multiplicative version of the Wiener index

The classical Wiener index, W(G), is equal to the sum of the distances between all pairs of vertexes of a (molecular) graph, G. We now consider a related topological index, pi(G), equal to the product of distances between all pairs of vertexes of G. The basic properties of the pi index are established and its possible physicochemical applications examined. In the case of alkanes, pi and W are highly correlated; a slightly curvilinear correlation exists between In pi and W.

Relation between distance-based topological indices.

The pi-index of the line graph of the molecular graph of an alkane is shown to be related to the pi, Harary, and reciprocal Wiener indices of that alkane. Thus a mathematical relation between several distance-based topological indices is obtained.