Ordering of alkane isomers by means of connectivity indices

The connectivity index of an organic molecule whose molecular graph is G is defined as C(lambda) = Sigma(delta(u)delta(v))(lambda), where delta(u) is the degree of the vertex u in G, where the summation goes over all pairs of adjacent vertices of G and where lambda is a pertinently chosen exponent. The usual value of lambda is -1/2, in which case chi = C(-1/2) is referred to as the Randie index. The ordering of isomeric alkanes according to chi follows the extent of branching of the carbon-atom skeleton, We now study the ordering of the constitutional isomers of alkanes with 6 through 10 carbon atoms with respect to C(lambda) for various values of the parameter lambda. This ordering significantly depends on lambda. The difference between the orderings with respect to chi and with respect to C(lambda) is measured by a function Delta and the lambda-dependence of Delta was established.