On K-Banhatti indices and entropy measure for rhodium (III) chloride via linear regression models

Mazhar Hussain; Muhammad Kamran Siddiqui; Muhammad Farhan Hanif; Hasan Mahmood; Zohaib Saddique; Samuel Asefa Fufa

doi:10.1016/j.heliyon.2023.e20935

On K-Banhatti indices and entropy measure for rhodium (III) chloride via linear regression models

Heliyon. 2023 Oct 16;9(10):e20935. doi: 10.1016/j.heliyon.2023.e20935. eCollection 2023 Oct.

Authors

Mazhar Hussain¹, Muhammad Kamran Siddiqui¹, Muhammad Farhan Hanif², Hasan Mahmood³, Zohaib Saddique⁴, Samuel Asefa Fufa⁵

Affiliations

¹ Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan.
² Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan.
³ Department of Mathematics, Government College University, Lahore, Pakistan.
⁴ Department of Chemistry, University of the Punjab, Quaid-i-Azam Campus Lahore, Pakistan.
⁵ Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia.

Abstract

Rhodium (III) chloride is a metallic compound characterized by its shiny and silvery-white appearance. It possesses high reflectivity and exhibits excellent resistance to corrosion. This makes it a popular choice for applications such as plating materials in jewelry and other decorative items, imparting a lustrous and reflective surface to the coated objects. Topological indices are numerical parameters employed to characterize the topology of a molecular structure. These indices are derived from the connectivity of atoms within the molecule and serve as predictors for various molecular properties, including reactivity, stability, and solubility. On the other hand, the Shannon entropy of a graph finds extensive applications in network science. It is utilized in the analysis of diverse networks, such as social networks, biological networks, and transportation networks. The Shannon entropy allows for the characterization of a network's topology and structure, aiding in the identification of crucial nodes or structures that play significant roles in network functionality and stability. In this paper, our primary objective is to compute different K-Banhatti indices and employ them to evaluate the entropy measure of Rhodium (III) chloride $R h C l_{3}$ . Additionally, we conducted an examination through linear regression analysis involving various indices and entropies associated with Rhodium chloride. Moreover, we established a correlation between degree-based Banhatti indices and entropies via the line fit method.

Keywords: Degree of vertex; Degree-based Banhatti indices; Rhodium chlorid; Shannon entropy.