Abstract

There are different mathematical tools to establish a numeric correlation between a chemical structure and its properties. A topological index is such a successful tool. It represents a graph in form of a single real number. In QSAR/QSPR study, the bioactivity of chemical compounds is predicted, using physico-chemical properties and topological indices. In this area of research, graph theory plays a vital role. The four operations on graphs were defined by Eliasi and Taeri in 2009. Imran et al. studied Cartesian product of the four operations on graph and computed bounds for some degree-based topological indices in 2017. In this paper, we extend this study for the lexicographic product of graphs to determine bounds of Zagreb indices, multiple Zagreb indices, and F-index for four sums of connected graphs.

摘要

有不同的数学工具可以建立化学结构与其性质之间的数字相关性。拓扑索引就是这样一种成功的工具。它以单个实数的形式表示图。在QSAR / QSPR研究中，使用理化性质和拓扑指数预测化合物的生物活性。在这一研究领域中，图论起着至关重要的作用。图上的四个操作由Eliasi和Taeri在2009年定义。研究了图中的四个运算的笛卡尔乘积并在2017年计算的一些基于度的拓扑指数范围在本文中，我们对图的字典积确定萨格勒布指数的范围，多萨格勒布指数，并延长这项研究˚F -四个连接图之和的索引。