Cut method for the multivariable Szeged-like polynomial with application to hyaluronic acid

Szeged-like topological indices are commonly studied distance-based molecular descriptors. These indices, together with related graph polynomials, offer valuable tools for characterising graph structures. Two new polynomials, the SMP polynomial and the edge-SMP polynomial, have been recently introduced and allow efficient computation of Szeged, Mostar, and PI indices (note that the abbreviation SMP comes from the names of these indices). In this paper, we develop the cut method to compute different versions of the SMP polynomial in a much more general way. In particular, the multivariable Szeged-like polynomial is introduced for any strength-weighted graph. Moreover, it is shown how it can be computed using strength-weighted quotient graphs obtained by a partition of the edge set coarser than the theta*-partition. The developed approach is demonstrated by calculating weighted-plus SMP polynomial and related topological indices for hyaluronic acid.