Study of middle graph for certain classes of graph by applying degree-based topological indices

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.