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On Some Topological Indices Defined via the Modified Sombor Matrix.
Xuewu Zuo1, Bilal Ahmad Rather2, Muhammad Imran2
1Department of Common Course, Anhui Xinhua University, Hefei 230088, China.
Molecules (Basel, Switzerland)
|October 14, 2022
Summary
This study introduces the modified Sombor index, spectral radius, and energy for graphs. It establishes bounds, characterizes extremal graphs, and identifies equienergetic chemical graphs.
Area of Science:
- Graph theory
- Mathematical chemistry
- Chemical graph theory
Background:
- The modified Sombor index, spectral radius, and energy are novel graph invariants.
- Understanding these invariants is crucial for analyzing molecular structures and properties.
Purpose of the Study:
- To derive bounds for the modified Sombor index, spectral radius, and energy.
- To characterize extremal graphs related to these invariants.
- To investigate modified Sombor equienergetic graphs and their relationship with chemical graph theory.
Main Methods:
- Theoretical derivations of bounds for graph invariants.
- Characterization of extremal graphs.
- Computational analysis using Mathematica and AutographiX.
- Regression analysis correlating graph invariants with boiling points.
Main Results:
- Several new bounds for the modified Sombor index, spectral radius, and energy are established.
- Extremal graphs for these invariants are characterized.
- A unique pair of modified Sombor equienergetic chemical graphs (order ≤ 7) was identified.
- A large class of modified Sombor equienergetic graphs, including regular and complete multipartite graphs with energy 2, was proven.
- Regression analyses showed correlations between modified Sombor indices and boiling points.
Conclusions:
- The study provides a comprehensive analysis of modified Sombor graph invariants.
- New insights into graph equienergetic properties and their chemical applications are presented.
- The findings contribute to the understanding of structure-property relationships in chemical graphs.
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