Computation of Certain Topological Indices of Nanotubes

Hayat, Sakander; Imran, Muhammad

doi:10.1166/jctn.2015.3699

Cited by 52 publications

(34 citation statements)

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“…1-3 9 11 12 For further study of these nanotubes see Refs. [5][6][7][8]. In this section, we calculate and work on anti-Kekulé number of two important families of nanotubes and we also discuss the anti-Kekulé number of CNC 2k n nanocones.…”

Section: Resultsmentioning

confidence: 99%

On the Anti-Kekulé Number of Nanotubes and Nanocones

Malik¹,

Hayat²,

Imran³

2015

j comput theor nanosci

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Let G V E be a connected graph. A set M ⊆ E is called a matching if no two edges in M have a common end-vertex. A matching M in G is perfect if every vertex of G is incident with an edge in M. The perfect matchings correspond to Kekulé structures which play an important role in the analysis of resonance energy and stability of hydrocarbons. The anti-Kekulé number of a graph G, denoted as ak G , is the smallest number of edges which must be removed from a connected graph G with a perfect matching, such that the remaining graph stay connected and contains no perfect matching. The anti-Kekulé numbers of silicate, oxide and honeycomb networks were calculated in [Xavier, Shanthi, and Raja, International Journal of Pure and Applied Mathematics 6, 1019 (2013)].In this paper, we calculate the anti-Kekulé number of HAC 5 C 7 2p q , T UC 4 C 8 R 2p q , ∀ p q ∈ nanotubes and CNC 2k n , ∀ k n ∈ nanocones. We set the infinite cases of all nanotubes as conjecture.

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Section: Resultsmentioning

confidence: 99%

On the Anti-Kekulé Number of Nanotubes and Nanocones

Malik¹,

Hayat²,

Imran³

2015

j comput theor nanosci

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“…and indices for some families of nanostar dendrimers and polyphenylene dendrimers are discussed in [20,21,24]. For a detailed description, their properties and bounds of the molecular topological indices of various classes of graph, see [24][25][26][27][28][29][30][31][32]. In this paper, we give an explicit formula of the and indices for certain nanostar dendrimers, namely PAMAM, tetrathiafulvalene and POPAM dendrimers.…”

Section: Resultsmentioning

confidence: 99%

On Topological Indices of Certain Families of Nanostar Dendrimers

et al. 2016

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Abstract:A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR)/quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Randić connectivity index, atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are used to predict the bioactivity of different chemical compounds. A dendrimer is an artificially manufactured or synthesized molecule built up from the branched units called monomers. In this paper, the fourth version of ABC index and the fifth version of GA index of certain families of nanostar dendrimers are investigated. We derive the analytical closed formulas for these families of nanostar dendrimers. The obtained results can be of use in molecular data mining, particularly in researching the uniqueness of tested (hyper-branched) molecular graphs.

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“…Imran et al studied various degree based topological indices for various networks like silicates, hexagonal, honeycomb and oxide in [14]. For further study of topological indices of various graph families see, [2,9,10,12,13,15,18,[22][23][24][25]29,31,37]. …”

Section: Resultsmentioning

confidence: 99%

Computing topological indices of Sudoku graphs

Gao

Imran

Baig

et al. 2016

J. Appl. Math. Comput.

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In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC) and geometric-arithmetic (G A) 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 indices of certain interconnection networks were studied recently by Imran et al. (Appl Math Comput 244:936-951, 2014). In this paper, we extend this study to n × n Sudoku graphs and derive analytical B Mohammad Reza Farahani

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Computation of Certain Topological Indices of Nanotubes

Cited by 52 publications

References 0 publications

On the Anti-Kekulé Number of Nanotubes and Nanocones

On the Anti-Kekulé Number of Nanotubes and Nanocones

On Topological Indices of Certain Families of Nanostar Dendrimers

Computing topological indices of Sudoku graphs

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