A variety of molecular-graph-based structure-descriptors were proposed, in particular the Wiener index W , the largest graph eigenvalue 1 , the connectivity index , the graph energy E and the Hosoya index Z, capable of measuring the branching of the carbon-atom skeleton of organic compounds, and therefore suitable for describing several of their physico-chemical properties. We now determine the structure of the chemical trees (= the graph representation of acyclic saturated hydrocarbons) that are extremal with respect to W , 1 , E, and Z, whereas the analogous problem for was solved earlier. Among chemical trees with 5, 6, 7, and 3k + 2 vertices, k = 2 3 : : : , one and the same tree has maximum 1 and minimum W , E, Z. Among chemical trees with 3k and 3k + 1 vertices, k = 3 4 : : : , one tree has minimum W and maximum 1 and another minimum E and Z.