Bipolar fuzzy outerplanar graphs approach in image shrinking

Abstract

Bipolar fuzzy outerplanar graphs are interesting and significant subclasses within the broader field of fuzzy graph theory. In this paper, bipolar fuzzy outerplanar graphs, and its properties are introduced. The subgraphs of bipolar fuzzy outerplanar graphs are identified by removing few vertices or edges from the bipolar fuzzy graphs. Additionally, both maximum and maximal bipolar fuzzy outerplanar subgraphs are explored with respect to vertex and edge deletion, using examples for illustration. Several relationships among the discussed concepts are expressed as theorems and conclusions. Further, bipolar fuzzy dual graph which is closely related to bipolar fuzzy outerplanar graphs is also described with interesting properties. These properties and characteristics help in understanding and utilizing bipolar fuzzy outerplanar graphs in various applications and research areas. In conclusion, we presented the use of bipolar fuzzy outerplanar graphs for the purpose of image shrinking.