On Acyclic Structures with Greatest First Gourava Invariant

Imtiaz, Mariam; Naseem, Maria; Arshad, Misbah; Kanwal, Salma; Liaqat, Maria

doi:10.1155/2022/6602899

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…Wang et al [17] obtained the maximum value of the Gourava indices for trees with given independence numbers. Mariam et al [18] provided an upper bound for the first Gourava index of trees with a given order, size, diameter, and pendant vertices. Basavanagoud et al [19,20] determined the Gourava and hyper-Gourava indices of cactus chains and suggested the applications of Gourava indices to the octane isomers.…”

Section: Introductionmentioning

confidence: 99%

Extremal Gourava indices of unicyclic graphs

Yuxin,

Zhou,

Qifan

2023

Preprint

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Topological indices are useful molecular descriptors to measure Quantitative Structure-Activity Relationship (QSAR), Quantitative Structure-Property Relationship (QSPR) and Quantitative Structure-Toxicity Relationship (QSTR). Recently, some novel topological indices of graphs, called the first Gourava index ($CO_1$) and the second Gourava index ($CO_2$), have been proposed to characterize the nature of chemical compounds or interconnection networks. The first and the second Gourava indices of the graph $G$ are denoted by $C{O_1}(G) =\sum\limits_{uv \in E(G)} {[{d_u}} + {d_v} + {d_u}{d_v}]$ and $C{O_2}(G) = \sum\limits_{uv \in E(G)} {[({d_u}} + {d_v}){d_u}{d_v}]$, where $d_u$ is the degree of vertex $u$. In this work, we investigate the extremal values on the first and the second Gourava indices of $n$-vertex unicyclic graphs and characterize the unicyclic graphs that achieve the extremes. We show that, for $n$-vertex unicyclic graph $G$, $8n \le C{O_1}(G) \le 2{n^2} - n + 9$ and $16n \le C{O_2}(G) \le n^3 +3n + 12$, where the lower bound is achieved by $C_n$ and the upper bound is achieved by $G_{3,1}^{(n)}$, which is obtained by attaching $n- 3$ leaves to one vertex of $C_3$. Furthermore, we investigate the applications of Gourava indices to the benzenoid hydrocarbons and show that they can predict the physico-chemical properties of molecules precisely.

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Section: Introductionmentioning

confidence: 99%

Extremal Gourava indices of unicyclic graphs

Yuxin,

Zhou,

Qifan

2023

Preprint

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“…Tis article has been retracted by Hindawi following an investigation undertaken by the publisher [1]. Tis investigation has uncovered evidence of one or more of the following indicators of systematic manipulation of the publication process:…”

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confidence: 99%

Retracted: On Acyclic Structures with Greatest First Gourava Invariant

2023

Journal of Chemistry

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On Trees with Given Independence Numbers with Maximum Gourava Indices

et al. 2023

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In mathematical chemistry, molecular descriptors serve an important role, primarily in quantitative structure–property relationship (QSPR) and quantitative structure–activity relationship (QSAR) studies. A topological index of a molecular graph is a real number that is invariant under graph isomorphism conditions and provides information about its size, symmetry, degree of branching, and cyclicity. For any graph N, the first and second Gourava indices are defined as GO1(N)=∑u′v′∈E(N)‍(d(u′)+d(v′)+d(u′)d(v′)) and GO2N=∑u′v′∈EN‍du′+dv′du′dv′, respectively.The independence number of a graph N, being the cardinality of its maximal independent set, plays a vital role in reading the energies of chemical trees. In this research paper, it is shown that among the family of trees of order δ and independence number ξ, the spur tree denoted as Υδ,ξ maximizes both 1st and 2nd Gourava indices, and with these characterizations this graph is unique.

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On Acyclic Structures with Greatest First Gourava Invariant

Abstract: Let ξ be a simple connected graph. The first Gourava index of graph ξ is defined as G O 1 … Show more

Cited by 3 publications

References 12 publications

Extremal Gourava indices of unicyclic graphs

Extremal Gourava indices of unicyclic graphs

Retracted: On Acyclic Structures with Greatest First Gourava Invariant

On Trees with Given Independence Numbers with Maximum Gourava Indices

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