Distance-based topological indices of nanosheets, nanotubes and nanotori of $$\hbox {SiO}_2$$ SiO 2

Arockiaraj, Micheal; Klavžar, Sandi; Mushtaq, Shagufa; Balasubramanian, K.

doi:10.1007/s10910-018-0956-8

Cited by 31 publications

(16 citation statements)

References 51 publications

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“…Now, with the help of the SiO 2 layer structure, another structure can be designed, which is known as the C 8 layer structure with an (s, p) dimension, by removing the vertices of degree 1 and their associated edges from the layer structure of SiO 2 having an (s, p) dimension to form a C 8 layer structure (see Figure 3). Some topological indices of this structure are discussed in 54 . Suppose

scriptG

is an C 8 layer structure, and it has

∣ V ((), G) ∣ = 3 sp + 2 ((), normals + normalp) + 1

and

∣ E ((), G) ∣ = 4 sp + 2 ((), normals + normalp)

.…”

Section: Mostar Indices Of C8 Layer Structurementioning

confidence: 99%

Mostar indices of SiO₂ nanostructures and melem chain nanostructures

Akhter

Imran

Iqbal

2020

Int J of Quantum Chemistry

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Very recently, a bond‐additive topological invariant, known as the Mostar index, has been described as a measure of peripherality in networks and graphs. Since then, more versions of this index have been introduced and named the total Mostar index and the edge Mostar index. In this paper, we derive the Mostar indices of SiO2 nanostructures and C8 layer structures. Furthermore, we have also provided results related to the Mostar indices of melem chain nanostructures.

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scriptG

is an C 8 layer structure, and it has

∣ V ((), G) ∣ = 3 sp + 2 ((), normals + normalp) + 1

and

∣ E ((), G) ∣ = 4 sp + 2 ((), normals + normalp)

.…”

Section: Mostar Indices Of C8 Layer Structurementioning

confidence: 99%

Mostar indices of SiO₂ nanostructures and melem chain nanostructures

Akhter

Imran

Iqbal

2020

Int J of Quantum Chemistry

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“…It is formed by merging the pendant edges along the right and left sides of the octagonal mesh of an SiO 2 nanosheet of dimension

(p, q - 1)

to form a tubular structure with length p and circumeference q . The structure of SiO 2 nanotube with p rows and q columns shown in the Figure clearly has

| V (G) | = q (3 p + 4)

vertices and

| E (G) | = 4 q (p + 1)

edges …”

Section: Computation Of We and Wve For Certain Molecular Structuresmentioning

confidence: 99%

“…Let G be a partial cube with

Θ

‐classes

F_{i} = {u_{j} v_{j} : 1 \leq j \leq s}

. It has been proved in the paper that if

| F_{i} | \geq 3

, then the quotient graph is K 2 with vertex‐strength‐weighted values

(n_{1} (F_{i}), m_{1} (F_{i}))

and

(n_{2} (F_{i}), m_{2} (F_{i}))

and edge‐strength value

| F_{i} |

as shown in the Figure (a). The

Θ^{*}

‐classes of

S u b (G)

are then

F_{_{i}}^{'} = {u_{j} x_{j}, x_{j} v_{j} : 1 \leq j \leq s}

, the corresponding quotient graph being the complete bipartite graph

K_{2, | F_{i} |}

with edge‐strength 1 for all the edges and vertex‐strength‐weighted values for one partite vertices as

(a_{i} (F_{_{i}}^{'}), b_{i} (F_{_{i}}^{'}))

and

(c_{i} (F_{_{i}}^{'}), d_{i} (F_{_{i}}^{'}))

and the other partite vertices (1,0) each as shown in the Figure (b) where

a_{i} (F_{_{i}}^{'}) = n_{1} (F_{i}) + m_{1} (F_{i})

b_{i} (F_{<...>}

…”

Section: We and Wve Of Subdivisions Of Partial Cubesmentioning

confidence: 99%

Edge Distance‐based Topological Indices of Strength‐weighted Graphs and their Application to Coronoid Systems, Carbon Nanocones and SiO₂ Nanostructures

Arockiaraj¹,

Klavžar

Clement³

et al. 2019

Molecular Informatics

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The edge-Wiener index is conceived in analogous to the traditional Wiener index and it is defined as the sum of distances between all pairs of edges of a graph G. In the recent years, it has received considerable attention for determining the variations of its computation. Motivated by the method of computation of the traditional Wiener index based on canonical metric representation, we present the techniques to compute the edge-Wiener and vertex-edge-Wiener indices of G by dissecting the original graph G into smaller strength-weighted quotient graphs with respect to Djoković-Winkler relation. These techniques have been applied to compute the exact analytic expressions for the edge-Wiener and vertex-edge-Wiener indices of coronoid systems, carbon nanocones and SiO 2 nanostructures. In addition, we have reduced these techniques to the subdivision of partial cubes and applied to the circumcoronene series of benzenoid systems.

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“…To aid in this endeavor, computation of the topological indices of the molecular graphs of candidate frameworks has proven to be a useful tool. In fact, topological indices of molecular graph families have a long history of contributing to the developmental process; for example, consider [5][6][7][8][9][10]. While other important computational studies have been carried out on various zeolite frameworks [2,11], computation of the most important topological indices has not yet occurred.…”

Section: Introductionmentioning

confidence: 99%

On certain distance and degree based topological indices of Zeolite LTA frameworks

Prabhu

Murugan²,

Cary

et al. 2020

Mater. Res. Express

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Zeolites are aluminosilicates with extensive application both commercially and in materials science. Current applications include dehydrating natural gas and in humidity sensors. Synthesis of new frameworks is an important area of research in chemistry and materials science. The Zeolite LTA framework in particular is getting much attention in this area due to its potential for application. Topological indices are graph invariants which provide information on the structure of graphs and have proven very useful in quantitative structure activity relationships (QSAR) and quantitative structure property relationships (QSPR) at predicting important chemico-phyiscal aspects of chemical compounds. In this paper we compute nine of the most significant distance based topological indices of the Zeolite LTA framework and thirteen valency based molecular descriptors. OPEN ACCESS RECEIVED

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Distance-based topological indices of nanosheets, nanotubes and nanotori of $$\hbox {SiO}_2$$ SiO 2

Cited by 31 publications

References 51 publications

Mostar indices of SiO₂ nanostructures and melem chain nanostructures

Mostar indices of SiO₂ nanostructures and melem chain nanostructures

Edge Distance‐based Topological Indices of Strength‐weighted Graphs and their Application to Coronoid Systems, Carbon Nanocones and SiO₂ Nanostructures

On certain distance and degree based topological indices of Zeolite LTA frameworks

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Distance-based topological indices of nanosheets, nanotubes and nanotori of $$\hbox {SiO}_2$$ SiO 2

Cited by 31 publications

References 51 publications

Mostar indices of SiO2 nanostructures and melem chain nanostructures

Mostar indices of SiO2 nanostructures and melem chain nanostructures

Edge Distance‐based Topological Indices of Strength‐weighted Graphs and their Application to Coronoid Systems, Carbon Nanocones and SiO2 Nanostructures

On certain distance and degree based topological indices of Zeolite LTA frameworks

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Product

Resources

About

Mostar indices of SiO₂ nanostructures and melem chain nanostructures

Mostar indices of SiO₂ nanostructures and melem chain nanostructures

Edge Distance‐based Topological Indices of Strength‐weighted Graphs and their Application to Coronoid Systems, Carbon Nanocones and SiO₂ Nanostructures