On topological properties of dominating David derived networks (original) (raw)
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Eccentricity-Based Topological Invariants of Dominating David-Derived Networks
Journal of Chemistry
A topological index is a numerical descriptor of the molecular structure based on certain topological features of the corresponding molecular graph. Topological indices are scientific contemplations of a graph that outline its subatomic topology and are graph-invariant. In a QSAR/QSPR study, topological indices are utilized to anticipate the physico-concoction resources and bioactivity of compounds. In this paper, we study some distance-based topological indices such as eccentric connectivity index (ECI), total eccentricity index (TEI), and eccentricity-based Zagreb index for dominating David-derived networks (DD network) and provide exact formulae of the said indices. These outcomes are valuable to organize the science of hidden topologies of this network.
Several Characterizations on Degree-Based Topological Indices for Star of David Network
Journal of Mathematics
In order to make quantitative structure-movement/property/danger relations, topological indices (TIs) are the numbers that are related to subatomic graphs. Some fundamental physicochemical properties of chemical compounds, such as breaking point, protection, and strain vitality, correspond to these TIs. In the compound graph hypothesis, the concept of TIs was developed in view of the degree of vertices. In investigating minimizing exercises of Star of David, these indices are useful. In this study, we explore the different types of Zagreb indices, Randić indices, atom-bond connectivity indices, redefined Zagreb indices, and geometric-arithmetic index for the Star of David. The edge partitions of this network are tabled based on the sum of degrees-of-end vertices and the sum of degree-based edges. To produce closed formulas for some degree-based network TIs, these edge partitions are employed.
Eccentricity-Based Topological Invariants of First Type of Dominating David-Derived Networks
Journal of Mathematics, 2023
Previous research has shown a substantial correlation between a chemical compound's molecular structure and its chemical characteristics. Understanding the physical characteristics and biological functions of biomolecules can be improved with the aid of topological indices based on their molecular structure. Eccentricity-connectivity indices, which describe molecular structures based on distance, have been applied to the mathematical modelling of a wide range of biological activities. In this article, we compute the exact formulae of various versions of the eccentricity-connectivity index for first type of Dominating David-derived network. The findings can be applied to computer-aided molecular design methods in pharmaceutical engineering.
Scientific Reports
Chemical graph theory is a well-established discipline within chemistry that employs discrete mathematics to represent the physical and biological characteristics of chemical substances. In the realm of chemical compounds, graph theory-based topological indices are commonly employed to depict their geometric structure. The main aim of this paper is to investigate the degree-based topological indices of dominating David derived networks (DDDN) and assess their effectiveness. DDDNs are widely used in analyzing the structural and functional characteristics of complex networks in various fields such as biology, social sciences, and computer science. We considered the FN*, {M}_{2}^{*}M2∗,andM 2 ∗ , andM2∗,and{HM}_{N}$$ HM N topological indices for DDDNs. Our computations' findings provide a clear understanding of the topology of networks that have received limited study. These computed indices exhibit a high level of accuracy when applied to the investigation of QSPRs and QSARs, as they de...
On topological indices of certain interconnection networks
Applied Mathematics and Computation, 2014
In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić , atom-bond connectivity ðABCÞ and geometric-arithmetic ðGAÞ index are used to predict the bioactivity of chemical compounds. A topological index is actually designed by transforming a chemical structure into a numeric number. These topological indices correlate certain physico-chemical properties like boiling point, stability, strain energy etc of chemical compounds. Graph theory has found a considerable use in this area of research. The topological properties of certain networks are studied recently in [13] by Hayat and Imran (2014). In this paper, we extend this study to interconnection networks and derive analytical closed results of general Randić index R a ðGÞ for different values of ''a'' for butterfly and Benes networks. We also compute first Zagreb, ABC, and GA indices for these important classes of networks. Moreover, we construct two new classes of mesh derived networks by using some basic operations of graphs on m  n mesh networks, and then study certain topological indices for these classes of networks.
On Degree-Based Topological Indices of Symmetric Chemical Structures
Symmetry
A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randi c ´ , atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randi c ´ index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.
On the Degree-Based Topological Indices of Some Derived Networks
Mathematics
There are numeric numbers that define chemical descriptors that represent the entire structure of a graph, which contain a basic chemical structure. Of these, the main factors of topological indices are such that they are related to different physical chemical properties of primary chemical compounds. The biological activity of chemical compounds can be constructed by the help of topological indices. In theoretical chemistry, numerous chemical indices have been invented, such as the Zagreb index, the Randić index, the Wiener index, and many more. Hex-derived networks have an assortment of valuable applications in drug store, hardware, and systems administration. In this analysis, we compute the Forgotten index and Balaban index, and reclassified the Zagreb indices, A B C 4 index, and G A 5 index for the third type of hex-derived networks theoretically.
On molecular topological properties of diamond-like networks
Canadian Journal of Chemistry, 2017
The Randić (product) connectivity index and its derivative called the sum-connectivity index are well-known topological indices and both of these descriptors correlate well among themselves and with the π-electronic energies of benzenoid hydrocarbons. The general n connectivity of a molecular graph G is defined as [Formula: see text] and the n sum connectivity of a molecular graph G is defined as [Formula: see text], where the paths of length n in G are denoted by [Formula: see text] and the degree of each vertex vi is denoted by di. In this paper, we discuss third connectivity and third sum-connectivity indices of diamond-like networks and compute analytical closed results of these indices for diamond-like networks.
On certain topological indices of silicate, honeycomb and hexagonal networks
In the QSAR /QSPR study, physicochemical properties and topological indices such as Randić, Zagreb, and ABC index are used to predict bioactivity of the chemical compounds. Graph theory has found considerable use in Chemistry, particularly in modeling chemical structures. Topological indices are designed basically by transforming a molecular graph into a number. In this paper we calculate the Randić, Zagreb, and ABC index of Silicate, honeycomb and hexagonal networks.