Abstract
The concept of a crisp graph is essential in the study of outerplanar graphs because outerplanar graphs are a unique type of planar graphs containing special characteristics. One of the core concepts of crisp graphs, the notion of a subgraph, is utilized primarily to solve difficult data problems. In this paper, researching outerplanar graphs in fuzzy graphs is the main aim of the work. By allowing edges connecting vertices to have varying levels of membership or fuzziness, a fuzzy graph is a mathematical framework that develops on the concept of crisp graphs. Because of their capacity to describe unclear or imprecise relationships between items, fuzzy outerplanar graphs might have potential applications. The subgraphs of fuzzy outerplanar graphs are revealed by eliminating specific vertices or edges from the fuzzy graphs. Furthermore, maximum, and maximal fuzzy outerplanar subgraphs defined for both vertex and edge deletion are examined using examples. Some of the connections between the concepts discussed are represented as theorems and conclusions. An application for the layout of a bypass road is discussed using the proposed concepts.
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