More on Sombor Index of Graphs

The study of the topological indices in the quantitative structure–activity and structure–property models are used to predict the physicochemical properties of the chemical compounds. In this paper, we analyze the molecular structure of hyaluronic acid conjugated with methotrexate which is used in anticancer drugs. We obtain the exact formulas for several new Sombor‐type vertex‐degree‐based topological indices and the Banhatti–Sombor‐type vertex‐degree‐based topological indices of the molecular structure of hyaluronic acid–methotrexate conjugate using the graph theory and the edge‐partition approach. We use Matlab and Mathematica software to evaluate the results and accuracy of calculations. The numerical results in this study can help understand the biological activity of the chemical structure of these drugs.

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“…Ning et al [37] introduced the increased Sombor index as follows

{SO}^{1} ((), G) goodbreak= \sum_{italicuv \in E} \sqrt{{(d (u) + 1)}^{2} + {(d (v) + 1)}^{2}},

…”

Section: Introductionmentioning

confidence: 99%

Degree‐based topological indices of the molecular structure of hyaluronic acid–methotrexate conjugates in cancer treatment

Movahedi

Akhbari

2023

Int J of Quantum Chemistry

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“…Sombor index of a graph

G = (V, E)

is denoted by

S O (G)

and define as

S O (G) = \sum_{x y \in E (G)} \sqrt{n_{x}^{2} + n_{y}^{2}}

where

n_{x}

and

n_{y}

are degrees of vertices

x, y

respectively [8]. On sombor indices, the reader can access some of the earlier works [9–13]. Many approaches can be used to compute graph invariants from the molecular graph.…”

Section: Introductionmentioning

confidence: 99%

On sombor indices of tetraphenylethylene, terpyridine rosettes and QSPR analysis on fluorescence properties of several aromatic hetero‐cyclic species

Rauf,

Ahmad

2023

Int J of Quantum Chemistry

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Aromatic heterocyclic compounds have received a lot of interest due to their various important medicinal and biological applications. The broad synthetic investigation and functional usefulness of heterocyclic molecules is driving a surge in research interest. They are found in more than 90% of innovative medications and bridge the gap between biology and chemistry, where so much scientific discovery and application happens. Heterocycles are also useful in a variety of domains, including pharmaceutical chemistry, biochemistry, and others. In this article, quantitative structure‐property relationship (QSPR) models is developed using sombor indices to predict fluorescence properties of aromatic hetero‐cyclic species based on their structural features. This allows researchers to estimate the fluorescence behavior of new molecules without performing experimental measurements. As an application, we have computed the sombor indices for self‐assembled supramolecular graphs made of terpyridine (TPE) and tetraphenylethylene (TPY) molecules that are produced as rosette cycles. This form of rosettes graph is used in electrical sensors, light emitting diodes, bioimaging and photoelectric devices, and so on. Tetraphenylethylene can be used to make fluorescent probes for next‐generation sensing applications with typical induced aggregative emission behavior.

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“…Successful predictive potential of the Sombor index has also been employed for simulating the thermodynamic characteristics of organic compounds. The reader is referred to [1][2][3][4][5][6][7][8][9][10][11]13,[16][17][18][19][20][21][22][23][24]26,27,30], for a detailed mathematical treatment of the Sombor index of graphs.…”

Section: Introductionmentioning

confidence: 99%

“…After its chemical applicability was reported, the Sombor index has been studied by mathematicians as well as theoretical chemists. Various mathematical properties of the Sombor index have been reported, for instance, in [2,4,6,7,8,9,10,11,12,14,16,17,18,22,24,25,26,27,29,30,31,32,33,35,36,42,44].…”

Section: Introductionmentioning

confidence: 99%

On Sombor Index of Graphs with a Given Number of Cut-Vertices

Hayat¹,

Rehman²

2022

MATCH

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Introduced by Gutman in 2021, the Sombor index is a novel graph-theoretic topological descriptor possessing potential applications in the modeling of thermodynamic properties of compounds. Let H k n be the family of graphs on order n and k number of cutvertices having at least one cycle. In this paper, we present minimum Sombor indices of graphs in H k n. The corresponding extremal graphs have been characterized as well.

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More on Sombor Index of Graphs

Cited by 11 publications

References 15 publications

Degree‐based topological indices of the molecular structure of hyaluronic acid–methotrexate conjugates in cancer treatment

Degree‐based topological indices of the molecular structure of hyaluronic acid–methotrexate conjugates in cancer treatment

On sombor indices of tetraphenylethylene, terpyridine rosettes and QSPR analysis on fluorescence properties of several aromatic hetero‐cyclic species

On Sombor Index of Graphs with a Given Number of Cut-Vertices

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