On the bounds of degree-based topological indices of the Cartesian product of F-sum of connected graphs

Imran, Muhammad; Baby, Shakila; Siddiqui, Hafız Muhammad Afzal; Shafiq, Muhammad Kashif

doi:10.1186/s13660-017-1579-5

Cited by 13 publications

(6 citation statements)

References 16 publications

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“…e bond-additive TIs have several applications; for example, they are useful in pharmaceutical sciences, in the prediction of physical properties of a molecule, and in complex network theory [14,15]. To study further topological properties of various chemical compounds, we refer to [16,17].…”

Section: Introductionmentioning

confidence: 99%

Mostar Index of Cycle-Related Structures

Asif

Kashif

Zafar

et al. 2022

Journal of Chemistry

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A topological index is a numerical quantity associated with the molecular structure of a chemical compound. This number remains fixed with respect to the symmetry of a molecular graph. Diverse research studies have shown that the topological indices of symmetrical graphs are interrelated with several physiochemical properties such as boiling point, density, and heat of formation. Peripherality is also an important tool to study topological aspects of molecular graphs. Recently, a bond-additive topological index called the Mostar index that measures the peripherality of a graph is investigated which attained wide attention of researchers. In this article, we compute the Mostar index of cycle-related structures such as the Jahangir graph and the cycle graph with chord.

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Section: Introductionmentioning

confidence: 99%

Mostar Index of Cycle-Related Structures

Asif

Kashif

Zafar

et al. 2022

Journal of Chemistry

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“…To connect with various physico-mix characteristics, Zagreb indices have required deep control upon the essentialness of the dendrimers [22]. e Zagreb polynomials were determined to happen for computation of the π-electron imperativeness of the particles inside specific brutal verbalizations [23,24].…”

Section: Applications Of Graph Theory Concept and Topological Indices In Chemistrymentioning

confidence: 99%

Sharp Bounds for the Inverse Sum Indeg Index of Graph Operations

Rani

Imran

Ali

2021

Mathematical Problems in Engineering

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Vukičević and Gasperov introduced the concept of 148 discrete Adriatic indices in 2010. These indices showed good predictive properties against the testing sets of the International Academy of Mathematical Chemistry. Among these indices, twenty indices were taken as beneficial predictors of physicochemical properties. The inverse sum indeg index denoted by ISI G k of G k is a notable predictor of total surface area for octane isomers and is presented as ISI G k = ∑ g k g k ′ ∈ E G k d G k g k d G k g k ′ / d G k g k + d G k g k ′ , where d G k g k represents the degree of g k ∈ V G k . In this paper, we determine sharp bounds for ISI index of graph operations, including the Cartesian product, tensor product, strong product, composition, disjunction, symmetric difference, corona product, Indu–Bala product, union of graphs, double graph, and strong double graph.

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“…Ali et al [40], Jamil et al [41], and Elumalai et al [42] computed bounds on zeroth order general Randić index for certain type of graphs. Later on, Deng et al [43], Imran et al [44], Liu et al [45], and Ahmad et al computed the first Zagreb index and second Zagreb index (general Randić index for exactly α � 1) of the F-sum graphs, bounds of several indices of the F-sum graphs, first generalized Zagreb indices of the F-sum graphs, and bounds on general sum-connectivity index for F-sum graphs [46], respectively. Moreover, Liu et al [45] proposed the open problem to compute the general Randić index for any α ∈ R. In this paper, we solve this open problem, partially, by computing the lower and upper bounds on general Randić index for the F-sum graphs for any α ∈ N.…”

Section: Journal Of Mathematicsmentioning

confidence: 99%

Bounds on General Randić Index for F-Sum Graphs

Ahmad

Javaid

et al. 2020

Journal of Mathematics

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A topological invariant is a numerical parameter associated with molecular graph and plays an imperative role in the study and analysis of quantitative structure activity/property relationships (QSAR/QSPR). The correlation between the entire π-electron energy and the structure of a molecular graph was explored and understood by the first Zagreb index. Recently, Liu et al. (2019) calculated the first general Zagreb index of the F-sum graphs. In the same paper, they also proposed the open problem to compute the general Randić index RαΓ=∑uv∈EΓdΓu×dΓvα of the F-sum graphs, where α∈R and dΓu denote the valency of the vertex u in the molecular graph Γ. Aim of this paper is to compute the lower and upper bounds of the general Randić index for the F-sum graphs when α∈N. We present numerous examples to support and check the reliability as well as validity of our bounds. Furthermore, the results acquired are the generalization of the results offered by Deng et al. (2016), who studied the general Randić index for exactly α=1.

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On the bounds of degree-based topological indices of the Cartesian product of F-sum of connected graphs

Cited by 13 publications

References 16 publications

Mostar Index of Cycle-Related Structures

Mostar Index of Cycle-Related Structures

Sharp Bounds for the Inverse Sum Indeg Index of Graph Operations

Bounds on General Randić Index for F-Sum Graphs

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