A topological index of G is a quantity related to G that characterizes its topology. Properties of the chemical compounds and topological invariants are related to each other. In this paper, we derive the algebraic polynomials including first and second Zagreb polynomials, and forgotten polynomial for Pm+FPm. Further, we worked on the hyper-Zagreb, first and second multiple Zagreb indices, and forgotten index of these graphs. Consider the molecular graph with atoms to be taken as vertices and bonds can be shown by edges. For such graphs, we can determine the topological descriptors showing their bioactivity as well as their physiochemical characteristics. Moreover, we derive graphical representation of our outcomes, depicting the technical dependence of topological indices and polynomials on the involved structural parameters.