A New Alternative to Szeged, Mostar, and PI Polynomials—The SMP Polynomials

Szeged-like topological indices are well-studied distance-based molecular descriptors, which include, for example, the (edge-)Szeged index, (edge-)Mostar and (vertex-)PI index. For these indices, corresponding polynomials were also defined, i.e., polynomial, Mostar PI etc. It is well known that, by evaluating first derivative of such a polynomial at x=1, we obtain related The aim this paper to introduce investigate new graph two variables, called SMP that all three vertex versions above-mentioned can be easily calculated using polynomial. Moreover, define edge-SMP edge version Various properties studied on some basic families graphs, extremal problems considered, several open stated. Then, focus Cartesian product, show how (edge-)SMP product n graphs (weighted) its factors.