Distance-based topological indices of the tree-like polyphenyl systems

Chen, Ailian; Xiong, Xianzhu; Lin, Fenggen

doi:10.1016/j.amc.2016.01.057

Cited by 5 publications

(2 citation statements)

References 34 publications

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“…Note that some of the results stated in Corollary 1 were already derived elsewhere (for example, see [16,41]). However, in our case these formulas are obtained by using a different approach, i.e.…”

Section: Para-polyphenyl Chainsmentioning

confidence: 63%

Generalized Cut Method for Computing Szeged–Like Polynomials with Applications to Polyphenyls and Carbon Nanocones

Brezovnik¹,

Tratnik²

2023

match

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Szeged, Padmakar-Ivan (PI), and Mostar indices are some of the most investigated distance-based Szeged-like topological indices. On the other hand, the polynomials related to these topological indices were also introduced, for example the Szeged polynomial, the edgeSzeged polynomial, the PI polynomial, the Mostar polynomial, etc. In this paper, we introduce a concept of the general Szeged-like polynomial for a connected strength-weighted graph. It turns out that this concept includes all the above mentioned polynomials and also infinitely many other graph polynomials. As the main result of the paper, we prove a cut method which enables us to efficiently calculate a Szeged-like polynomial by using the corresponding polynomials of strength-weighted quotient graphs obtained by a partition of the edge set that is coarser than Θ∗ -partition. To the best of our knowledge, this represents the first implementation of the famous cut method to graph polynomials. Finally, we show how the deduced cut method can be applied to calculate some Szeged-like polynomials and corresponding topological indices of para-polyphenyl chains and carbon nanocones.

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Section: Para-polyphenyl Chainsmentioning

confidence: 63%

Generalized Cut Method for Computing Szeged–Like Polynomials with Applications to Polyphenyls and Carbon Nanocones

Brezovnik¹,

Tratnik²

2023

match

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“…Papers [1,4,22,[25][26][27] present a sample of relevant recent investigations on the mentioned distance-based topological indices.…”

Section: Introductionmentioning

confidence: 99%

The Edge-Wiener Index, the Szeged Indices and the PI Index of Benzenoid Systems in Sub-Linear Time

Črepnjak¹,

Tratnik²

2017

Preprint

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In this paper, we investigate the edge-Wiener index, the Szeged index, the edge-Szeged index, and the PI index, which are some of the most studied distance-based topological indices. As the main result we show that for benzenoid systems these indices can be computed in sub-linear time with respect to the number of vertices. More precisely, they can be computed in the time dependent on the length of the boundary cycle of a benzenoid system.

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Several distance and degree-based molecular structural attributes of cove-edged graphene nanoribbons

Prabhu,

Murugan,

Imran

et al. 2024

Heliyon

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Distance-based topological indices of the tree-like polyphenyl systems

Cited by 5 publications

References 34 publications

Generalized Cut Method for Computing Szeged–Like Polynomials with Applications to Polyphenyls and Carbon Nanocones

Generalized Cut Method for Computing Szeged–Like Polynomials with Applications to Polyphenyls and Carbon Nanocones

The Edge-Wiener Index, the Szeged Indices and the PI Index of Benzenoid Systems in Sub-Linear Time

Several distance and degree-based molecular structural attributes of cove-edged graphene nanoribbons

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