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Optimizing hybrid network topologies in communication networks through irregularity strength.
Syed Aqib Abbas Naqvi1, Faraha Ashraf1, Ali Ovais2
1School of Mathematics, Minhaj University Lahore, Lahore, Pakistan.
Scientific Reports
|August 11, 2025
Summary
This study applies graph labeling, specifically H-irregularity strength, to optimize hybrid local area network (LAN) topologies. It introduces novel graph models for improved network efficiency, scalability, and security.
Area of Science:
- Graph Theory Applications
- Communication Network Design
- Network Topology Optimization
Background:
- Local Area Networks (LANs) face challenges in scalability, traffic optimization, and security.
- Hybrid network topologies require advanced design and analysis methods.
- Graph theory offers a powerful framework for modeling complex network structures.
Purpose of the Study:
- To propose graph labeling techniques, particularly H-irregularity strength, for modeling and optimizing hybrid LAN topologies.
- To explore the application of specialized graphs like Dutch Windmill and Corona product graphs in network design.
- To provide theoretical insights for enhancing communication efficiency, scalability, and security in LANs.
Main Methods:
- Utilized graph labeling techniques, focusing on H-irregularity strength.
- Modeled hybrid LAN topologies using Dutch Windmill and Corona product graphs.
- Calculated edge, vertex, and total H-irregularity strength for these specific graph families.
Main Results:
- Demonstrated the interaction between theoretical graph labeling and practical network technology.
- Provided theoretical findings on how labeling schemes can model network behavior, improve resource allocation, and trace data flow.
- Calculated irregularity strength for Dutch Windmill and Corona product graphs, offering new perspectives for hybrid LAN representation.
Conclusions:
- Graph labeling, specifically H-irregularity strength, offers a viable mathematical framework for optimizing hybrid LAN topologies.
- The proposed models provide a theoretical foundation for improving network performance, scalability, and security.
- Further research involving simulations and empirical validation is recommended for practical implementation.
Keywords:
Corona product graphsDutch windmill graphEdge H-irregularity strengthIrregularity strengthsTotal H-irregularity strengthVertex H-irregularity strengthMore Related Videos
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