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Sombor topological indices for different nanostructures.

Muhammad Imran1, Rashad Ismail2, Muhammad Azeem1

  • 1Department of Mathematics, Riphah International University Lahore, Pakistan.

Heliyon
|October 23, 2023
PubMed
Summary

This study introduces novel Sombor graph indices derived from Euclidean geometry. These new graph parameters are applied to analyze various nanotube Y-junctions.

Keywords:
Degree–based topological descriptorsGeometric indicesNano-junctionsNanostructuresSombor descriptors

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Area of Science:

  • Mathematics
  • Graph Theory
  • Nanotechnology

Background:

  • The Sombor graph parameter, defined as the sum of degrees of adjacent vertices, is a recent development in graph theory.
  • Euclidean geometry provides a framework for defining graph invariants and understanding their properties.
  • Nanotube Y-junctions are complex structures with potential applications in materials science and electronics.

Purpose of the Study:

  • To introduce and define new types of Sombor indices using Euclidean geometry.
  • To investigate the application of these newly developed Sombor indices to various nanotube Y-junctions.
  • To establish geometrical interpretations for the Sombor graph parameters and their invariants.

Main Methods:

  • Application of Euclidean geometry to define Sombor graph parameters and their invariants.
  • Introduction of the first area-based Sombor index using geometric principles.
  • Construction of the second, fourth, and sixth Sombor graph parameters utilizing the concept of angular orientation.
  • Development of the third and fifth Sombor graph parameters based on perimeter calculations.

Main Results:

  • Novel Sombor indices were successfully defined and geometrically interpreted.
  • The first area-based Sombor index was introduced.
  • New Sombor graph parameters were constructed using angular orientation and perimeter.
  • The developed Sombor indices were applied to analyze various nanotube Y-junctions.

Conclusions:

  • The study successfully extended the concept of Sombor indices through Euclidean geometry.
  • The introduced Sombor indices provide new tools for analyzing the properties of nanotube Y-junctions.
  • Geometrical interpretations offer deeper insights into the structure-property relationships of these graph parameters.