Study on geometric–arithmetic, arithmetic–geometric and Randić indices of graphs

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-09-18 DOI:10.1016/j.dam.2024.09.007

Kinkar Chandra Das , Da-yeon Huh , Jayanta Bera , Sourav Mondal

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引用次数: 0

Abstract

Topological indices are mathematical descriptors used in the field of chemistry to characterize the topological structure of chemical compounds. The Randić index ( $R$ ), the geometric–arithmetic index ( $G A$ ), and the arithmetic–geometric index ( $A G$ ) represent three widely recognized topological indices. In most scenarios, the properties of $A G$ and $G A$ exhibit opposing tendencies. Furthermore, it is observed that, $A G (G) > R (G)$ and $G A (G) > R (G)$ for any given graph $G$ . Our focus is thus directed towards investigating the gaps between $A G$ and $R$ , as well as $G A$ and $R$ . We find that the invariants $A G - R$ and $G A - R$ correlate well with some molecular properties. Numerous upper and lower bounds for the quantities $A G - R$ and $G A - R$ are computed for general graphs, bipartite graphs, chemical graphs, trees, and chemical trees, in terms of graph order, with an emphasis on characterizing extremal graphs.

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图形的几何指数、算术指数和兰迪克指数研究

拓扑指数是化学领域用来描述化合物拓扑结构的数学描述符。兰迪克指数（R）、几何-算术指数（GA）和算术-几何指数（AG）是三种广为认可的拓扑指数。在大多数情况下，AG 和 GA 的属性表现出相反的趋势。此外，我们还观察到，对于任何给定的图 G，AG(G)>R(G)和 GA(G)>R(G)。因此，我们的重点是研究 AG 和 R 以及 GA 和 R 之间的差距。我们根据图的阶数计算了一般图、二叉图、化学图、树和化学树的 AG-R 和 GA-R 量的大量上界和下界，重点是极值图的特征。

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.