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Network design for bypass roads using interval valued fuzzy outerplanar graphs.

Deivanai Jaisankar¹, Sujatha Ramalingam², Nagarajan Deivanayagampillai³

¹Mathematics, School of Science and Humanities, Shiv Nadar University Chennai, Rajiv Gandhi Salai (OMR), Chengalpattu District, Kalavakkam, 603110, Tamil Nadu, India.

Scientific Reports

|September 30, 2025

Summary

This study introduces interval valued fuzzy outerplanar graphs (IVFOGs) for bypass road network design. This approach effectively manages traffic uncertainties to optimize routes and improve urban mobility.

Keywords:

Bypass road network Interval valued fuzzy dual graphs Interval valued fuzzy graph Interval valued maximum and maximal fuzzy outerplanar subgraphs VD and ED interval valued fuzzy outerplanar subgraphs

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Area of Science:

Graph Theory
Transportation Engineering
Fuzzy Set Theory

Background:

Increasing vehicular growth and evolving lifestyles necessitate advanced road network designs.
Urban traffic regulation faces challenges due to inherent uncertainty and variability.
Existing models may not adequately address imprecise traffic parameters.

Purpose of the Study:

To present a novel approach for bypass road network design using interval valued fuzzy outerplanar graphs (IVFOGs).
To manage uncertainty and variability in urban traffic regulation using interval valued fuzzy sets.
To analyze structural properties of IVFOGs and their duals for modeling bypass networks.

Main Methods:

Application of interval valued fuzzy sets to capture imprecise traffic parameters.
Investigation of structural properties of IVFOGs and their duals.
Exploration of vertex and edge deletion concepts for route optimization.
Analysis of maximal and maximum interval valued fuzzy outerplanar graphs.

Main Results:

A theoretical foundation for modeling bypass networks using IVFOGs.
Identification of optimal bypass routes that avoid urban congestion through vertex and edge deletion.
Demonstration of maximal and maximum IVFOGs via examples.
Development of an uncertainty-tolerant model for road transport planning.

Conclusions:

The proposed IVFOG framework offers a flexible and uncertainty-tolerant model for bypass road network design.
This approach enhances urban mobility and optimizes commuter travel time.
The study contributes to more efficient and effective road transport planning in complex urban environments.