On the Wiener Polarity Index of Lattice Networks

Chen, Lin; Tao, Li; Liu, Jinfeng; Shi, Yongtang; Wang, Hua

doi:10.1371/journal.pone.0167075

Cited by 21 publications

(11 citation statements)

References 47 publications

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“…The Wiener polarity index of fullerenes and hexagonal systems was studied in Behmaram et al [19]. The Wiener polarity index of square, hexagonal and triangular lattices were studied in Chen et al [20]. Recently, Arockiaraj et al [21] studied the hyper‐Wiener and Wiener polarity indices of silicate and oxide networks.…”

Section: Motivation and Important Resultsmentioning

confidence: 99%

Wiener polarity index and related molecular topological descriptors of titanium oxide nanotubes

Imran

Malik

Javed

2021

Int J of Quantum Chemistry

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The relations between the physico‐chemical properties of a chemical compounds its molecular structure properties are used in quantitative structure activity and property relationship studies by using graph‐theoretical techniques. The Wiener polarity index is the number of unordered pairs of vertices lying at distance 3 in a graph. This index is correlated to the cluster coefficient of chemical networks. The Wiener polarity index has been used to exhibit quantitative structure–property relationships in a series of acyclic and cycle‐containing hydrocarbons. In this paper, we consider three variants of the graph of titanium oxide TiO2, that is, two‐dimensional lattice, nanotubes and nanotorus. For all these graphs, we compute the number of pairs of vertices lying at distance one, two and three. Using this information, we compute the Wiener polarity index and leap Zagreb indices of these graphs.

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Section: Motivation and Important Resultsmentioning

confidence: 99%

Wiener polarity index and related molecular topological descriptors of titanium oxide nanotubes

Imran

Malik

Javed

2021

Int J of Quantum Chemistry

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“…The Wiener polarity index of a graph G is defined as

W_{P} ((), G) = ∣ ({}, ({}, u, v) : d_{G} ((), u, v) = 3, u, v \in V ((), G)) ∣ .

It was observed [28] that

W_{P} ((), G) = \frac{1}{2} \sum_{v \in V ((), G)} ∣ N_{G}^{3} ((), v) ∣

and the importance of W P has been demonstrated in various papers (see References [29, 30] for details). Suppose G is an acyclic graph, it was realized [31] that

W_{P} ((), G) = \sum_{italicuv \in E ((), G)} ((), d_{u} - 1) \times ((), d_{v} - 1) .

If G is a C 3 ‐free and C 4 ‐free graph such that its different cycles have at most one common edge [30],

W_{P} ((), G) = M_{2} ((), G) - M_{1} ((), G) + ∣ E ((), G) ∣ - 5 N_{P} ((), G) - 3 N_{h} ((), G),

and that if G is a C 3 ‐free graph such that its different cycles have at most one common edge [29],

W_{P} ((), G) = M_{2} ((), G) - M_{1} ((), G) + ∣ E ((), G) ∣ - 5 N_{p} ((), G) - 3 N_{h} ((), G) -

…”

Section: Wiener Polarity Indicesmentioning

confidence: 99%

Distance based and bond additive topological indices of certain repurposed antiviral drug compounds tested for treating COVID‐19

Liu

Arockiaraj²,

Arulperumjothi

et al. 2021

Int J of Quantum Chemistry

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The entire world is struggling to control the spread of coronavirus (COVID-19) as there are no proper drugs for treating the disease. Under clinical trials, some of the repurposed antiviral drugs have been applied to COVID-19 patients and reported the efficacy of the drugs with the diverse inferences. Molecular topology has been developed in recent years as an influential approach for drug design and discovery in which molecules that are structurally related show similar pharmacological properties. It permits a purely mathematical description of the molecular structure so that in the development of identification of new drugs can be found through adequate topological indices. In this paper, we study the structural properties of the several antiviral drugs such as chloroquine, hydroxychloroquine, lopinavir, ritonavir, remdesivir, theaflavin, nafamostat, camostat, umifenovir and bevacizumab by considering the distance and bond measures of chemical compounds. Our quantitative values of the topological indices are extremely useful in the recent development of designing new drugs for COVID-19.

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“…Tratnik gave a generalization of the results given in and applied his results to obtain a closed formula for the Wiener polarity index of phenylenes. Chen et al introduced a simple formula for computing the Wiener polarity number of a simple graph and for more information on this topic, we refer the interested readers to the papers for more information on this topic.…”

Section: Introductionmentioning

confidence: 99%