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.
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