Comparative study of domination parameters with the π‐electronic energy of benzenoid hydrocarbons

Khan, Suliman

doi:10.1002/qua.27192

Cited by 3 publications

(5 citation statements)

References 30 publications

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“…We present an application of

in structure-property modeling of the total π -electronic energy of benzenoid hydrocarbons. This, in turn, answers positively to Problem 1 by Khan [28] .…”

Section: Discussionmentioning

confidence: 54%

“…Results are explained with help of some examples. The second part of the paper solves an open problem in Khan (2023) [28] which asks to find a domination-related parameter which delivers a correlation coefficient of

0.9967

with the total π -electronic energy of lower benzenoid hydrocarbons. We show that the locating-dominating number

delivers such a strong prediction potential.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Locating-dominating number of certain infinite families of convex polytopes with applications

Hayat,

Kartolo,

Khan

et al. 2024

Heliyon

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“…We present an application of

in structure-property modeling of the total π -electronic energy of benzenoid hydrocarbons. This, in turn, answers positively to Problem 1 by Khan [28] .…”

Section: Discussionmentioning

confidence: 54%

0.9967

with the total π -electronic energy of lower benzenoid hydrocarbons. We show that the locating-dominating number

delivers such a strong prediction potential.…”

mentioning

confidence: 99%

Locating-dominating number of certain infinite families of convex polytopes with applications

Hayat,

Kartolo,

Khan

et al. 2024

Heliyon

View full text Add to dashboard Cite

“…In the last section, we introduced and studied symmetric γ-endowed graphs. In the second part of the paper, we found a domination-based parameter which showcases a correlation value of ρ = 0.99905 with E π (β) of lower BHs, thus answering an open problem in [34]. The following problems are naturally raised from the findings of this study.…”

Section: Discussionmentioning

confidence: 59%

“…In a recent work, Khan [34] carried out a comparison analysis of seven dominationdependent graphical descriptors (excluding Γ), aiming to establish correlations with the E π of lower BHs. Among these parameters, the work by Khan [34] showcased that the paired-domination number γ p exhibits the most significant capability, showing a high correlation number of ρ = 0.9967. The following question was raised by concluding the investigation.…”

Section: Application Of γ In Qspr Modelsmentioning

confidence: 99%

“…We also introduce and study the symmetric γ-endowed graphs and prove some structurally important results. In this work, an open problem (from Khan [34]) asking to find a domination-dependent graphical descriptor delivering a correlation coefficient of ρ > 0.9967 with the total π-electronic energy E π of lower benzenoid hydrocarbons (BHs) has been solved. Section 6 shows that the upper domination number studied in this paper delivers a correlation coefficient ρ = 0.99905 > 0.9967 with E π of lower BHs.…”

Section: Introductionmentioning

confidence: 99%

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Characterizations of Minimal Dominating Sets in γ-Endowed and Symmetric γ-Endowed Graphs with Applications to Structure-Property Modeling

Hayat,

Sundareswaran,

Shanmugapriya

et al. 2024

Symmetry

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Claude Berge (1987) introduced the concept of k-extendable graphs, wherein any independent set of size k is inherently a constituent of a maximum independent set within a graph H=(V,E). Graphs possessing the property of being 1-extendable are termedas Berge graphs. This introduction gave rise to the notion of well-covered graphs and well-dominated graphs. A graph is categorized as well-covered if each of its maximal independent sets is, in fact, a maximum independent set. Similarly, a graph attains the classification of well-dominated if every minimal dominating set (DS) within it is a minimum dominating set. In alignment with the concept of k-extendable graphs, the framework of (k,γ)-endowed graphs and symmetric (k,γ)-endowed graphs are established. In these graphs, each DS of size k encompasses a minimum DS of the graph. In this article, a study of γ-endowed dominating sets is initiated. Various results providing a deep insight into γ-endowed dominating sets in graphs such as those characterizing the ones possessing a unique minimum DS are proven. We also introduce and study the symmetric γ-endowed graphs and minimality of dominating sets in them. In addition, we give a solution to an open problem in the literature. which seeks to find a domination-based parameter that has a correlation coefficient of ρ>0.9967 with the total π-electronic energy of lower benzenoid hydrocarbons. We show that the upper dominating number Γ(H) studied in this paper delivers a strong prediction potential.

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On degree-based operators and topological descriptors of molecular graphs and their applications to QSPR analysis of carbon derivatives

Khan,

Bhatti,

Tawfiq

et al. 2024

Sci Rep

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This work initiates a concept of reduced reverse degree based -Polynomial for a graph, and differential and integral operators by using this -Polynomial. In this study twelve reduced reverse degree-based topological descriptors are formulated using the -Polynomial. The topological descriptors, denoted as ’s, are numerical invariants that offer significant insights into the molecular topology of a molecular graph. These descriptors are essential for conducting QSPR investigations and accurately estimating physicochemical attributes. The structural and algebraic characteristics of the graphene and graphdiyne are studied to apply this methodology. The study involves the analysis and estimation of Reduced reverse degree-based topological descriptors and physicochemical features of graphene derivatives using best-fit quadratic regression models. This work opens up new directions for scientists and researchers to pursue, taking them into new fields of study.

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Comparative study of domination parameters with the π‐electronic energy of benzenoid hydrocarbons

Cited by 3 publications

References 30 publications

Locating-dominating number of certain infinite families of convex polytopes with applications

Locating-dominating number of certain infinite families of convex polytopes with applications

Characterizations of Minimal Dominating Sets in γ-Endowed and Symmetric γ-Endowed Graphs with Applications to Structure-Property Modeling

On degree-based operators and topological descriptors of molecular graphs and their applications to QSPR analysis of carbon derivatives

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