Topological indices are well-known molecular descriptors that may be applied to any graph and to model specific molecular structures, utilized for property correlation in quantitative structure activity and property relationship (QSAR and QSPR) analyses. Strong methods for machine learning information and thermodynamic simulations of massive networks and nanomaterials can be facilitated by using topological indices. Kekulenes are a novel type of cycloarenes, arranged in doughnut-shaped cyclic benzene rings with riveting superaromaticity and other significant properties. The main aim of this paper is to ascertain the notable degree and the neighborhood degree sum-based indices through M-polynomials and neighborhood M-polynomials of certain types of tessellations of kekulenes. Then, a graphical comparison of the resulting indices is also performed.