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Topological indices are graph invariants numeric quantities, which areutilized by researchers to analyze a variety of physiochemical aspects ofmolecules. The goal of developing topological indices is to give each chemicalstructure a numerical value while maintaining the highest level ofdifferentiation. Using these indices, the classification of various structures,and their physiochemical and biological properties can be predicted. In thispaper, the leap and leap hyper Zagreb indices, as well as their polynomials fora zigzag benzenoid system $Z_{p}$ and a rhombic benzenoid system $R_{p}$ aredetermined. In addition, new $k$-distance degree-based topological indices suchas leap-Somber index, hyper leap forgotten index, leap $Y$ index, and leap $Y$coindex are also computed for the molecular graphs of $Z_p$ and $R_p$.Furthermore, their numerical computation and discussion are performed todetermine the significance of their physiochemical properties.

On k-distance degree based topological indices of benzenoid systems