Valency-based topological descriptors of chemical networks and their applications

Hayat, Sakander; Wang, Shaohui; Liu, Jia‐Bao

doi:10.1016/j.apm.2018.03.016

Cited by 60 publications

(41 citation statements)

References 25 publications

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“…Chen showed that R α with α = −.2661 and SCI α with α = −.5601 have the best correlation coefficient with the π ‐electronic energies of lower benzenoid hydrocarbons. However, recently Hayat et al studied the performance of all well‐known degree‐based topological indices and showed that R and SCI indices are not preferable for QSAR and QSPR studies. It was also shown that the only general Randić connectivity and general sum‐connectivity indices, which are preferable for QSAR and QSPR studies are R α with α = −1 and SCI α with α = −3.…”

Section: Introductionmentioning

confidence: 99%

“…It was also shown that the only general Randić connectivity and general sum‐connectivity indices, which are preferable for QSAR and QSPR studies are R α with α = −1 and SCI α with α = −3. In this scenario, the study by Hayat et al shows that the work by Lučić et al and Chen are of nominal importance when it comes to study the practical applicability of these degree‐bases indices.…”

Section: Introductionmentioning

confidence: 99%

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Correlation between the Estrada index and π‐electronic energies for benzenoid hydrocarbons with applications to boron nanotubes

Hayat

Imran

Liu

2019

Int J of Quantum Chemistry

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In this article, we present an efficient computer-based computational technique to compute the energy and Estrada index of graphs. It is shown that our computational method is more efficient and bears less computational and algorithmic complexity. We use our method to show the main result of this article, which asserts that the Estrada index correlates with the π-electronic energies of lower benzenoid hydrocarbons with correlation coefficient 0.9993. This enhances the practical applicability of the Estrada index and warrants its further usage in quantitative structure activity relationships. We further apply our computational technique in computing the energy and Estrada index of two infinite families of boron triangular nanotubes. We perform simulation based on certain computer software packages to study the graph-theoretic behavior of the obtained results. Our results help to correlate certain physicochemical properties of underlying chemical structures of these nanotubes. K E Y W O R D Sπ-electronic energy, benzenoid hydrocarbons, boron nanotubes, energy, Estrada index

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Correlation between the Estrada index and π‐electronic energies for benzenoid hydrocarbons with applications to boron nanotubes

Hayat

Imran

Liu

2019

Int J of Quantum Chemistry

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“…Xu et al [3] determined the eccentricity-based topological indices of graphs. Hayat et al [4] studied the valency-based topological descriptors of chemical networks and their applications. Let G + uv be the graph obtained from G by adding an edge uv ∈ E(G).…”

Section: Introductionmentioning

confidence: 99%

The Extremal Graphs of Some Topological Indices with Given Vertex k-Partiteness

Gao

Zhou

et al. 2018

Mathematics

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The vertex k-partiteness of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we characterize the extremal value of the reformulated first Zagreb index, the multiplicative-sum Zagreb index, the general Laplacian-energy-like invariant, the general zeroth-order Randić index, and the modified-Wiener index among graphs of order n with vertex k-partiteness not more than m .

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“…Then the codes of the outer vertices are ( ) = (ℎ 1 ( ), ℎ 2 ( ), ℎ 3 ( )) and the codes of the inner vertices are (V ) = ( 1 ( ), 2 ( ), 3 ( )), where Discrete Dynamics in Nature and Society Table 14: The code (V) of V with respect to = {V 4 , V 10 , V 13 } in (15,5). …”

Section: Theorem 11mentioning

confidence: 99%

“…Graph theory is a powerful tool to model the real world applications such as physical-chemical property testing [4,5]. Motivated by the problem of uniquely determining the location of an intruder in a network, the concept of metric dimension of a graph was introduced by Slater in [6], where the metric generators were called locating sets.…”

Section: Introductionmentioning

confidence: 99%

The Metric Dimension of Some Generalized Petersen Graphs

Shao

Sheikholeslami

et al. 2018

Discrete Dynamics in Nature and Society

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The distance ( , V) between two distinct vertices and V in a graph is the length of a shortest ( , V)-path in . For an ordered subset = { 1 , 2 , . . . , } of vertices and a vertex V in , the code of V with respect to is the ordered -tupleis a resolving set for if every two vertices of have distinct codes. The metric dimension of is the minimum cardinality of a resolving set of . In this paper, we first extend the results of the metric dimension of ( , 3) and ( , 4) and study bounds on the metric dimension of the families of the generalized Petersen graphs (2 , ) and (3 , ). The obtained results mean that these families of graphs have constant metric dimension.

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Valency-based topological descriptors of chemical networks and their applications

Cited by 60 publications

References 25 publications

Correlation between the Estrada index and π‐electronic energies for benzenoid hydrocarbons with applications to boron nanotubes

Correlation between the Estrada index and π‐electronic energies for benzenoid hydrocarbons with applications to boron nanotubes

The Extremal Graphs of Some Topological Indices with Given Vertex k-Partiteness

The Metric Dimension of Some Generalized Petersen Graphs

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