Study for Some Eccentricity-based Topological Indices of Second Type of Dominating David-derived Network

Jia-Bao Liu; Haidar Ali; Didar Abdulkhaleq Ali; Ayesha Umer; Parvez Ali; Syed Ajaz K Kirmani

doi:10.2174/1386207326666230831125646

Study for Some Eccentricity-based Topological Indices of Second Type of Dominating David-derived Network

Comb Chem High Throughput Screen. 2023 Aug 31. doi: 10.2174/1386207326666230831125646. Online ahead of print.

Authors

Jia-Bao Liu¹, Haidar Ali², Didar Abdulkhaleq Ali³, Ayesha Umer¹, Parvez Ali⁴, Syed Ajaz K Kirmani⁵

Affiliations

¹ Department of Mathematics, Riphah International University, Faisalabad Campus, Pakistan.
² School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China.
³ Department of Mathematics, Faculty of Science, University of Zakho, Zakho, Iraq.
⁴ Department of Mechanical Engineering, College of Engineering, Qassim University, Unaizah, Saudi Arabia.
⁵ Department of Electrical Engineering, College of Engineering, Qassim University, Unaizah, Saudi Arabia.

PMID: 37653626
DOI: 10.2174/1386207326666230831125646

Abstract

Background: Dominating David-derived networks are widely studied due to their fractal nature, with applications in topology, chemistry, and computer sciences. The use of molecular structure descriptors is a standard procedure that is used to correlate the biological activity of molecules with their chemical structures, which can be useful in the field of pharmacology.

Objective: This article's goal is to develop analytically closed computing formulas for eccentricity-based descriptors of the second type of dominating David-derived derived network. Thermodynamic characteristics, physicochemical properties, and chemical and biological activities of chemical graphs are just a few of the many properties that may be determined using these computation formulas.

Methods: Vertex sets were initially divided according to their degrees, eccentricities, and cardinalities of occurrence. The eccentricity-based indices are then computed using some combinatorics and these partitions.

Results: Total eccentricity, average eccentricity, and the Zagreb index are distance-based topological indices utilized in this study for the second type of dominating David-derived network, denoted as D_2 (m).

Conclusion: These calculations will assist the readers in estimating the fractal and difficult-to-handle thermodynamic and physicochemical aspects of chemical structure. Apart from configuration and impact resistance, the D_2 (m) design has been used for fundamental reasons in a variety of technical and scientific advancements.

Keywords: Average eccentricity; Eccentricity; Second type of dominating David-derived network $D_{2}(m)$; Total eccentricity; Zagreb index.