More on the line graph model for predicting physico-chemical properties of alkanes

The iterated line graph sequence L ⁱ , i=1,2,..., of a graph G is defined so that L ¹ is the line graph of G, L ² is the line graph of L ¹ , etc. Let G be a molecular graph possessing m ₀ edges and let m _i be the number of edges of L ⁱ , i=1,2,.... We examine the applicability of the linear model a ₀ m _i0 +a ₁ m _i1 + +a ₂ m _i2 +...+a _k m _ik +b for predicting physico-chemical properties of alkanes (boiling points, molar volumes, molar refractions, heats of vaporization, critical temperatures, critical pressures and surface tensions). For all properties studied, the optimal model has k=2, i ₀ =0, i ₁ =1, but i ₂ varies between 2 and 4.