Graph theory is a fundamental branch of mathematics that studies networks made up of nodes (vertices) and connections (edges). A key concept in graph theory is the intersection graph, where vertices represent sets, and edges are drawn between vertices if their corresponding sets intersect. A circular-arc graph specifically models the intersections of arcs on a circle, with vertices corresponding to the arcs and edges existing between intersecting arcs. This paper delves into the study of circular-arc graphs within the frameworks of fuzzy, intuitionistic fuzzy, neutrosophic, and Turiyam Neutrosophic graphs, all of which incorporate uncertainty into graph structures. Additionally, we examine the concept of proper circular-arc graphs. [ABSTRACT FROM AUTHOR]

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