Noureen Sadia, Ali Akbar, Bhatti Akhlaq A, Alanazi Abdulaziz M, Shang Yilun
Faculty of Science, University of Gujrat, Gujrat, Pakistan.
College of Science, University of Ha'il, Ha'il, Saudi Arabia.
Heliyon. 2024 May 15;10(10):e30913. doi: 10.1016/j.heliyon.2024.e30913. eCollection 2024 May 30.
Many existing studies show that there exists a strong relationship between structures and characteristics of molecules. Topological indices are often used in modeling the properties of chemical compounds and biological activities in theoretical chemistry. Topological indices are numerical values associated with structures of molecules in such a way that they remain constant under graph isomorphism. Multiplicative Zagreb indices are among the famous topological indices that have been explored by numerous researchers in the last few years. The first objective of the present paper is to examine the importance of general multiplicative Zagreb indices for forecasting the enthalpy of formation of hydrocarbons using a data set of 25 benzenoid hydrocarbons. The second objective of this paper is to study molecular trees with a given order and with a given number of branching vertices or segments using general multiplicative (first and second) Zagreb indices. Sharp lower/upper bounds on these Zagreb indices for the aforementioned molecular trees are obtained and the graphs attaining these bounds are determined. Bounds on the classical multiplicative Zagreb and Narumi-Katayama indices are corollaries of the obtained results.
许多现有研究表明，分子的结构与特性之间存在着紧密的关系。在理论化学中，拓扑指数常用于对化合物的性质和生物活性进行建模。拓扑指数是与分子结构相关的数值，其特点是在图同构下保持不变。乘法 Zagreb 指数是过去几年众多研究人员所探索的著名拓扑指数之一。本文的首要目标是利用一个包含 25 种苯型烃的数据集，研究通用乘法 Zagreb 指数在预测烃类生成焓方面的重要性。本文的第二个目标是使用通用乘法（第一和第二）Zagreb 指数来研究具有给定阶数以及给定数量分支顶点或边段的分子树。得到了上述分子树的这些 Zagreb 指数的精确上下界，并确定了达到这些界的图。经典乘法 Zagreb 指数和 Narumi - Katayama 指数的界是所得结果的推论。
