Topological invariants of sustainable network for energy efficiency and environmental impact reduction

Jun Yang; Hifza Iqbal; Muhammad Akmal; Muhammad Akhtar Tarar; Jun Yang; Hifza Iqbal; Muhammad Akmal; Muhammad Akhtar Tarar

doi:10.3934/math.2026573

AIMS Mathematics

2026, Volume 11, Issue 5: 13937-13962. doi: 10.3934/math.2026573

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Research article

Topological invariants of sustainable network for energy efficiency and environmental impact reduction

1.
School of Economics and Law, Chaohu University, Chaohu, China
2.
Department of Mathematics and Statistics, The University of Lahore, Defence Road Campus, Lahore, Pakistan
3.
Department of Civil Engineering, The University of Lahore, Defence Road Campus, Lahore, Pakistan

Received: 26 February 2026 Revised: 13 April 2026 Accepted: 17 April 2026 Published: 18 May 2026
MSC : 05C02, 05C90

In this work, we employ a graph-theoretical framework to study the structural characteristics of nanocarbon sheets. Key auxiliary properties are predicted using the Van, R, and S topological indices, which makes it easier to design materials that are both energy-efficient and environmentally friendly. The analysis assesses how topological characteristics can affect performance metrics that are important for long-term uses in green energy systems. Our results show how useful these descriptors are for simulating the behavior of sustainable nanomaterials based on nanocarbons and directing the creation of devices with lower power consumption and higher energy efficiency. Theoretical expressions are clearly visualized by the use of tables and three-dimensional MATLAB figures.
- sustainable network,
- topological index,
- nanostructure
Citation: Jun Yang, Hifza Iqbal, Muhammad Akmal, Muhammad Akhtar Tarar. Topological invariants of sustainable network for energy efficiency and environmental impact reduction[J]. AIMS Mathematics, 2026, 11(5): 13937-13962. doi: 10.3934/math.2026573

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Abstract

In this work, we employ a graph-theoretical framework to study the structural characteristics of nanocarbon sheets. Key auxiliary properties are predicted using the Van, R, and S topological indices, which makes it easier to design materials that are both energy-efficient and environmentally friendly. The analysis assesses how topological characteristics can affect performance metrics that are important for long-term uses in green energy systems. Our results show how useful these descriptors are for simulating the behavior of sustainable nanomaterials based on nanocarbons and directing the creation of devices with lower power consumption and higher energy efficiency. Theoretical expressions are clearly visualized by the use of tables and three-dimensional MATLAB figures.

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