20.500.12556/DKUM-87023 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, the (edge-)Mostar index, and the (vertex-)PI index. For these indices, the corresponding polynomials were also defined, i.e., the (edge-)Szeged polynomial, the Mostar polynomial, the PI polynomial, etc. It is well known that, by evaluating the first derivative of such a polynomial at x = 1, we obtain the related topological index. The aim of this paper is to introduce and investigate a new graph polynomial of two variables, which is called the SMP polynomial, such that all three vertex versions of the above-mentioned indices can be easily calculated using this polynomial. Moreover, we also define the edge-SMP polynomial, which is the edge version of the SMP polynomial. Various properties of the new polynomials are studied on some basic families of graphs, extremal problems are considered, and several open problems are stated. Then, we focus on the Cartesian product, and we show how the (edge-)SMP polynomial of the Cartesian product of n graphs can be calculated using the (weighted) SMP polynomials of its factors. SMP polynomial edge-SMP polynomial Cartesian product Szeged index Mostar index PI index polinomi kartezični produkt Szegedov indeks Mostarjev indeks true true true MDPI Angleški jezik Slovenski jezik Članek v reviji 2024-02-09 08:35:48 2024-02-09 08:54:00 2024-02-28 14:54:25 0000-00-00 00:00:00 2023 0 0 Str. 1-15 Št. 4, št. članka 956 Letn. 11 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2022-12-28 2023-02-10 2023-02-13 519.17 142045955 10.3390/math11040956 2227-7390 Knor-2023-A_New_Alternative_to_Szeged,_Mostar.pdf Knor-2023-A_New_Alternative_to_Szeged,_Mostar.pdf 1 0B5C8F35E284A379C2821416B44180F6 c34041e5b53ee40bf76bceaf88d97e7dabdf0b068e7d73f8d0f5b54c2d255edd 2b93b152-c720-11ee-a1af-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=176023 https://doi.org/10.3390/math11040956 0 3efabf55-c720-11ee-a1af-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=176024 Fakulteta za naravoslovje in matematiko 0 0 0