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Topological index is an important numerical magnitude that can reflect the whole structure of a graph. Degree-based indices are mathematical descriptors worked in chemical graph theory to compute the connectivity and underlying descriptions of molecules. These indices, such as the Wiener index, Randi´ c index, and Zagreb indices, are obtained from the quantities of vertices in molecular graphs. The Wiener index correspond to the calculation of gaps between all pairs of nodes in a graph, presenting information about molecular dimension and separating. Zagreb indices, including the first and second Zagreb indices, summarize the measure allocation and node connectivity within a molecular graph. Degree-based indices portray a critical position in molecular modeling, QSAR investigations, and medication layout, requiring perceptions into molecular regional anatomy and forecasting various physicochemical assets. In this article, we compute topological descriptors for complete p-ary trees. Interesting comparison of these indices are is also shown in tabular and graphical format. Moreover, expressions for multiple Zagreb indices and polynomials for these important classes are found.