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Bipolar fuzzy outerplanar graphs approach in image shrinking.

Deivanai Jaisankar¹, Sujatha Ramalingam², Nagarajan Deivanayagampillai³

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

Scientific Reports

|July 8, 2025

Summary

This study introduces bipolar fuzzy outerplanar graphs and their properties. These graphs are utilized for image shrinking applications, demonstrating their practical utility in fuzzy graph theory.

Keywords:

Bipolar fuzzy dual graphs Bipolar fuzzy graph Bipolar maximum and maximal fuzzy outerplanar subgraphs VD and ED bipolar fuzzy outerplanar subgraphs

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Area of Science:

Graph Theory
Fuzzy Mathematics
Computer Science

Background:

Bipolar fuzzy graphs are a significant area within fuzzy graph theory.
Outerplanar graphs are a well-studied class of graphs with specific structural properties.

Purpose of the Study:

To introduce and define bipolar fuzzy outerplanar graphs.
To explore the properties of these graphs and their subgraphs.
To investigate the application of bipolar fuzzy outerplanar graphs in image shrinking.

Main Methods:

Definition and characterization of bipolar fuzzy outerplanar graphs.
Identification of subgraphs through vertex and edge deletion.
Exploration of maximum and maximal bipolar fuzzy outerplanar subgraphs.
Description of the bipolar fuzzy dual graph and its properties.

Main Results:

The paper establishes theorems and conclusions regarding the relationships between bipolar fuzzy outerplanar graphs and their subgraphs.
Properties of maximum and maximal subgraphs are detailed with illustrative examples.
The bipolar fuzzy dual graph is presented as a related structure with unique characteristics.

Conclusions:

Bipolar fuzzy outerplanar graphs possess distinct properties that enhance understanding within fuzzy graph theory.
The study demonstrates a novel application of these graphs for image shrinking.
The research provides a foundation for further exploration and utilization of bipolar fuzzy outerplanar graphs in diverse fields.