A novel approach to determine the Sombor-type indices via M-polynomial

Topological indices can be interpreted as the mathematical characterizations of a molecular compound and are significantly employed to forecast its physical, chemical and biological information. Computation of topological indices of a graph through its associated graph polynomial is a modern and optimal approach. One such method is to determine the degree-based topological indices of a graph using its M-polynomial. Among the class of degree-based topological indices, the Sombor indices are one of the most investigated indices in recent times. In this article, the M-polynomial-based derivation formulas are derived to compute the different Sombor-type indices, namely the Sombor index, modified Sombor index, first and second Banhatti–Sombor indices, and their reduced form of the Sombor indices. Furthermore, our proposed derivation formulas are applied to compute the Sombor-type indices of the jagged-rectangle benzenoid system \(B_{m,n}\) $B_{m,n}$ . Additionally, the comparison among the Sombor-type indices of \(B_{m,n}\) $B_{m,n}$ is presented through numerical and graphical representations.