基于连接数的图笛卡尔积拓扑指标

IF 0.7 Q2 MATHEMATICS Muenster Journal of Mathematics Pub Date : 2023-05-13 DOI:10.1155/2023/8272936
Aiman Arshad, Aqsa Sattar, M. Javaid, Mamo Abebe Ashebo
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引用次数: 0

摘要

图论(graph theory, GT)的研究领域正在迅速扩大,并在化学信息学中发挥着重要的作用,主要是在数学和化学中发展出不同的物理化学、化学结构及其性质。利用数值结构不变量使化学图形细节的处理和研究成为可能。研究拓扑指数(TIs)的这些化学特性是通过数学化学学科来实现的。本文利用完全图和路径图的笛卡尔积研究了基于连接数(CN)的指数,即基于第一连接的萨格勒布指数(1st CBZI)、基于第二连接的萨格勒布指数(2nd CBZI)和基于第三连接的萨格勒布指数(3rd CBZI),然后修正基于第一连接的萨格勒布指数(CBZI)和第二、第三修正的CBZI。给出了完全图和路径图两种特殊图的一乘CBZI、二乘CBZI、三乘CBZI和四乘CBZI的一般结果。更准确地说,我们对这两个笛卡尔积的计算表达式进行了图形和数值分析。
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Connection Number- Based Topological Indices of Cartesian Product of Graphs
The area of graph theory (GT) is rapidly expanding and playing a significant role in cheminformatics, mostly in mathematics and chemistry to develop different physicochemical, chemical structure, and their properties. The manipulation and study of chemical graphical details are made feasible by using numerical structure invariant. Investigating these chemical characteristics of topological indices (TIs) is made possible by the discipline of mathematical chemistry. In this article, we study with the Cartesian product of complete graphs, with path graphs, and find their general result of connection number (CN)-based TIs, namely, first connection- based Zagreb index (1st CBZI), second connection- based Zagreb index (2nd CBZI), and third CBZI (3rd CBZI) and then modified first connection- based Zagreb index (CBZI) and second and third modified CBZIs. We also express the general results of first multiplicative CBZI, second multiplicative CBZI, and third and fourth multiplicative CBZI, of two special types of graphs, namely, complete graphs and path graphs. More precisely, we arrange the graphical and numerical analysis of our calculated expressions for both of Cartesian product with each other.
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