In an earlier work it was demonstrated that the Zenkevich index U provides a measure of the intramolecular energy of an organic molecule, and that - in the case of alkanes - it is related to the Wiener index. We now show that U is much closer related to the recently introduced variable Wiener index Wλ : Within sets of isomeric alkanes, the relation between U and Wλ is linear, the (U,Wλ )-points forming several, mutually parallel, lines. Each such line pertains to a group of isomers possessing a fixed number of methyl groups. There exists a critical value of the parameter λ for which all the (U,Wλ )-lines coalesce, in which case the relation between U and Wλ becomes independent of the number of methyl groups. Approximate analytical expressions for the (U,Wλ )-dependence are deduced.