Degree‐based topological indices of the molecular structure of hyaluronic acid–methotrexate conjugates in cancer treatment

Abstract

The study of the topological indices in the quantitative structure–activity and structure–property models are used to predict the physicochemical properties of the chemical compounds. In this paper, we analyze the molecular structure of hyaluronic acid conjugated with methotrexate which is used in anticancer drugs. We obtain the exact formulas for several new Sombor‐type vertex‐degree‐based topological indices and the Banhatti–Sombor‐type vertex‐degree‐based topological indices of the molecular structure of hyaluronic acid–methotrexate conjugate using the graph theory and the edge‐partition approach. We use Matlab and Mathematica software to evaluate the results and accuracy of calculations. The numerical results in this study can help understand the biological activity of the chemical structure of these drugs.

The Euler Sombor index of a graph

“…Consider Equation (6) and let ω i,j be a given function. Additionally, consider B i,j defined in Equation (7). Let all B i,j be negative and the following inequalities hold:…”

“…In the mathematical and chemical literature, several dozen of such vertex‐degree‐based descriptors (graph invariants) have been considered [1–3], some of which found noteworthy chemical and pharmacological applications [4–7], such as first Zagreb ($$$ {M}_1 $$$), second Zagreb ($$$ {M}_2 $$$), Albertson ($$$ Alb $$$), forgotten ($$$ F $$$), Sombor ($$$ SO $$$), and so forth.…”

Estimating physico-chemical properties of drugs for prostate cancer using degree-based and neighbourhood degree-based topological descriptors

“…Shahid Zaman et al [29] inspected on QSPR Analysis of some novel drugs used in blood cancer treatment via degree-based topological indices and regression models in 2023. Fateme Movahedi et al [30] examined degree-based topological indices of the molecular structure of hyaluronic acid-methotrexate conjugates in cancer treatment in 2023.…”

Geometric approach to vertex‐degree‐based topological indices–Elliptic Sombor index, theory and application

“…In the literature several dozen of such vertex-degree-based descriptors have been considered [1][2][3][4], some of which found noteworthy chemical and pharmacological applications, see for example, [5][6][7]. In what follows, a few among these indices will be mentioned: first Zagreb (M 1 ), second Zagreb (M 2 ), Albertson (Alb), forgotten (F), Sombor (SO), defined as:…”

“…In the literature several dozen of such vertex‐degree‐based descriptors have been considered [1–4], some of which found noteworthy chemical and pharmacological applications, see for example, [5–7]. In what follows, a few among these indices will be mentioned: first Zagreb ( M 1 ), second Zagreb ( M 2 ), Albertson ( Alb ), forgotten ( F ), Sombor ( SO ), defined as: $$...$$…”