On Topological Indices of OT [m, n] Octagonal Tillings and TiO2 Nanotubes

Afzal, Hafiz Usman; Fatima, Tahzeeb

doi:10.17344/acsi.2018.4897

Cited by 5 publications

(4 citation statements)

References 11 publications

(28 reference statements)

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“…Let G be the molecular graph of the crystallographic structure of TiO 2 [m, n, t] with m × n numbers of unit cells in the plane and t layers. In Figures 3 and 4 we have shown the graph of TiO 2 [1, 1, 1] and TiO 2 [3,3,3] respectively. The cardinality of vertices and edges of the given molecular graph TiO 2 [m, n, t] are (m + 1)(n + 1)(t + 1) + 5mnt + 2mt and 10mnt + 2m(n + 1)t + (m + 1) n (t + 1) respectively.…”

Section: Molecular Graph Of 𝐓𝐢𝐎 𝟐 Crystalmentioning

confidence: 99%

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On Degree Based Topological Indices of TiO2 Crystal via M-Polynomial

Baishya¹,

Bora²,

Chetri³

et al. 2022

Trends Sci

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Topological indices (TI) (descriptors) of a molecular graph are very much useful to study various physiochemical properties. It is also used to develop the quantitative structure-activity relationship (QSAR), quantitative structure-property relationship (QSPR) of the corresponding chemical compound. Various techniques have been developed to calculate the TI of a graph. Recently a technique of calculating degree-based TI from M-polynomial has been introduced. We have evaluated various topological descriptors for 3-dimensional TiO2 crystals using M-polynomial. These descriptors are constructed such that it contains 3 variables (m, n and t) each corresponding to a particular direction. These 3 variables facilitate us to deeply understand the growth of TiO2 in 1 dimension (1D), 2 dimensions (2D), and 3 dimensions (3D) respectively. HIGHLIGHTS Calculated degree based Topological indices of a 3D crystal from M-polynomial A relation among various Topological indices is established geometrically Variations of Topological Indices along three dimensions (directions) are shown geometrically Harmonic index approximates the degree variation of oxygen atom

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Section: Molecular Graph Of 𝐓𝐢𝐎 𝟐 Crystalmentioning

confidence: 99%

“…These studies are also known as molecular graphs [1,2]. A molecular graph is a simple graph in which the edges denote the chemical bonding while vertices denote the atoms in a given material structure [3]. Gao et al [4] discussed various TI w.r.t a family of anticancer drugs.…”

Section: Introductionmentioning

confidence: 99%

On Degree Based Topological Indices of TiO2 Crystal via M-Polynomial

Baishya¹,

Bora²,

Chetri³

et al. 2022

Trends Sci

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show abstract

“…A molecular network in terms of a graph is a portrayal of structural information of a chemical compound in which the atoms are displayed by vertices while the bonds are represented by edges between the vertices. The applications of TIs in various fields of science are boundless, as one can see in [5][6][7]. According to the reported literature, TIs have great importance in nanotechnology and theoretical chemistry.…”

Section: Introductionmentioning

confidence: 99%

Topological Aspects of Dendrimers via Connection-Based Descriptors

Javaid¹,

Alamer²,

Sattar³

2023

Computer Modeling in Engineering &Amp; Sciences

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Topological indices (TIs) have been practiced for distinct wide-ranging physicochemical applications, especially used to characterize and model the chemical structures of various molecular compounds such as dendrimers, nanotubes and neural networks with respect to their certain properties such as solubility, chemical stability and low cytotoxicity. Dendrimers are prolonged artificially synthesized or amalgamated natural macromolecules with a sequential layer of branches enclosing a central core. A present-day trend in mathematical and computational chemistry is the characterization of molecular structure by applying topological approaches, including numerical graph invariants. Among topological descriptors, Zagreb connection indices (ZCIs) have much importance. This manuscript involves the establishment of general results to calculate ZCIs, namely first ZCI (FZCI), second ZCI (SZCI), third ZCI (TZCI), modified FZCI, modified SZCI and modified TZCI of two special types of dendrimers nanostars, namely, poly propylene imine octamin (PPIO) dendrimer and poly (propyl) ether imine (PPEtIm) dendrimer. Furthermore, we provide the numerical and graphical comparative analysis of our calculated results for both types of dendrimers with each other.

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“…TIs are extensively used in the study of quantitative structure-activity relationships and quantitative structure-property relationships [38]. Many researchers have worked on TIs [1,18,25]. TIs are classified into three distinct TIs, namely, degree-based TI, distance-based TI, and polynomial-based TI.…”

Section: Introductionmentioning

confidence: 99%

Connection-Based Multiplicative Zagreb Indices of Dendrimer Nanostars

Sattar

Javaid

Bonyah³

2021

Journal of Mathematics

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The field of graph theory is broadly growing and playing a remarkable role in cheminformatics, mainly in chemistry and mathematics in developing different chemical structures and their physicochemical properties. Mathematical chemistry provides a platform to study these physicochemical properties with the help of topological indices (TIs). A topological index (TI) is a function that connects a numeric number to each molecular graph. Zagreb indices (ZIs) are the most studied TIs. In this paper, we establish general expressions to calculate the connection-based multiplicative ZIs, namely, first multiplicative ZIs, second multiplicative ZIs, third multiplicative ZIs, and fourth multiplicative ZIs, of two renowned dendrimer nanostars. The defined expressions just depend on the step of growth of these dendrimers. Moreover, we have compared our calculated for both type of dendrimers with each other.

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On Topological Indices of OT [m, n] Octagonal Tillings and TiO2 Nanotubes

Cited by 5 publications

References 11 publications

On Degree Based Topological Indices of TiO2 Crystal via M-Polynomial

On Degree Based Topological Indices of TiO2 Crystal via M-Polynomial

Topological Aspects of Dendrimers via Connection-Based Descriptors

Connection-Based Multiplicative Zagreb Indices of Dendrimer Nanostars

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