Copyright © 2023 by SPC.Topological indices are extremely useful for analyzing various physical and chemical properties associated with a chemical compound. A topological index describes molecular structures by converting them into certain real numbers. Topological indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity of molecule correlated with their chemical structure. The chemical shape of benzene molecule is very common in nano-science, chemistry, and physics. The circumcoronene collection of benzenoid (Hs) generates from the benzene molecules. Jahangir graph (J(m,t)) is a generalized wheel graph that consists of (m, t) circular vertices and a center vertex connected to every mt vertex on the circle. In this article, we will compute the topological indices of the middle graph of the circumcoronene series of benzenoids (Hs) and Jahangir graph (J(m,t)). In addition, comparison of the middle graph of the circumcoronene series of benzenoid (Hs) and Jahangir graph (J(3,t)) are presented numerically and graphically.