Comparing the excepted values of atom-bond connectivity and geometric–arithmetic indices in random spiro chains

Wei, Shouliu; Ke, Xiaoling; Hao, Guoliang

doi:10.1186/s13660-018-1628-8

Cited by 20 publications

(12 citation statements)

References 27 publications

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“…Several papers are concentrated about random arrangement of graphs. For more details, see [9][10][11][12][13][14][15]. The comparison and inequalities among some indices for molecular graphs have been derived in [16,17].…”

Section: Methodsmentioning

confidence: 99%

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Expected Values of Some Molecular Descriptors in Random Cyclooctane Chains

Raza

Imran

2021

Symmetry

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The modified second Zagreb index, symmetric difference index, inverse symmetric index, and augmented Zagreb index are among the molecular descriptors which have good correlations with some physicochemical properties (such as formation heat, total surface area, etc.) of chemical compounds. By a random cyclooctane chain, we mean a molecular graph of a saturated hydrocarbon containing at least two rings such that all rings are cyclooctane, every ring is joint with at most two other rings through a single bond, and exactly two rings are joint with one other ring. In this article, our main purpose is to determine the expected values of the aforementioned molecular descriptors of random cyclooctane chains explicitly. We also make comparisons in the form of explicit formulae and numerical tables consisting of the expected values of the considered descriptors of random cyclooctane chains. Moreover, we outline the graphical profiles of these comparisons among the mentioned descriptors.

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Section: Methodsmentioning

confidence: 99%

“…and by the recurrence relation (10) Proof. Since E R 2 = 183 10 is correct, then for m ≥ 3, there are 4 types of probabilities (see Figure 3).…”

mentioning

confidence: 97%

Expected Values of Some Molecular Descriptors in Random Cyclooctane Chains

Raza

Imran

2021

Symmetry

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“…We first introduce the technical notations and lemmas that will be used in the discussion. For more background information one may check [26,22,20,27].…”

Section: Preliminariesmentioning

confidence: 99%

The expected subtree number index in random polyphenylene and spiro chains

Sun

Jun

et al. 2020

Discrete Applied Mathematics

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The subtree number index STN(G) of a simple graph G is the number of nonempty subtrees of G. It is a structural and counting topological index that has received more and more attention in recent years. In this paper we first obtain exact formulas for the expected values of subtree number index of random polyphenylene and spiro chains, which are molecular graphs of a class of unbranched multispiro molecules and polycyclic aromatic hydrocarbons. Moreover, we establish a relation between the expected values of the subtree number indices of a random polyphenylene and its corresponding hexagonal squeeze. We also present the average values for subtree number indices with respect to the set of all polyphenylene and spiro chains with n hexagons.

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“…2 . There are few papers which focused on the random structure of a chemical graphs, see for example [19] , [20] and references therein. It was discovered that the algebraic structure count of a phenylene is equal to the number of Kekule structures of the associated hexagonal squeeze [21] , [22] .…”

Section: Introductionmentioning

confidence: 99%

The expected values of arithmetic bond connectivity and geometric indices in random phenylene chains

Raza

2020

Heliyon

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Phenylenes are a class of conjugated hydrocarbons composed of a special arrangement of six- and four-membered rings. In this paper, the expected values of the atom-bond connectivity (ABC), geometric-arithmetic (GA), and Zagreb indices of this class of conjugated hydrocarbons have been determined. At the end, the comparisons with respect to the random phenylene chains among the expected values of these indices, have been determined explicitly. The graphical profiles of these indices have been shown in order to support our results.

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Comparing the excepted values of atom-bond connectivity and geometric–arithmetic indices in random spiro chains

Cited by 20 publications

References 27 publications

Expected Values of Some Molecular Descriptors in Random Cyclooctane Chains

Expected Values of Some Molecular Descriptors in Random Cyclooctane Chains

The expected subtree number index in random polyphenylene and spiro chains

The expected values of arithmetic bond connectivity and geometric indices in random phenylene chains

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