In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index also known as a connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. These parameters also have applications in drug structures. In this paper, we give some new probabilistic results on the first Zagreb, the Platt, Narumi-Katayama and Gordon- Scantlebury indices in two bucket tree structures.
 P. Billingsley, Probability and Measure. John Wiley and Sons, New York, 1995.
 M. Gordon, and G. R. Scantlebury, Non-random polycondensation: statistical theory of the substitution effect, Trans. Faraday Soc. 60 (2), 1964, pp. 604-621.
 R. Kazemi, Depth in bucket recursive trees with variable capacities of buckets, Acta Math. Sin, English Series, 30(2), 2014, pp. 305-310.
 X. Li, Z. Li, and L. Wang, The inverse problems for some topological indices in combinatorial chemistry, J. Comput. Biol. 10, 2003, pp. 47-55.
 H. Mahmoud, and R. Smythe, Probabilistic analysis of bucket recursive trees, Theor. Comput. Sci. 144, 1995, pp. 221-249.
 Nikolic, R., Tolic, I. M., Trinajstí, I. M. and Baucic, I. On the Zagreb indices as complexity indices, Croatica Chemica Acta. 73, 2000, pp. 909-921.
 I. Nikolic, G. Kovacevic, A. Milicevic, and N. Trinajstic, On molecular complexity indices. In Complexity in Chemistry: Introduction and Fundamentals, eds D. Bonchev and D. H. Rouvray. Taylor and Francis, London, 2003.
 H. Narumi, and M. Katayama, Simple topological index. A newly devised index characterizing the topological nature of structural isomers of saturated hydrocarbons, Mem. Fac. Engin. Hokkaido Univ. 16, 1984, pp. 209-214.
 J. R. Platt, Inuence of neighbor bonds on additive bond properties in paraffins, Chem. Phys. 15, 1947, pp. 419-420.