Neutrosophic and Information Fusion NIF 2836-7863 10.54216/NIF https://www.americaspg.com/journals/show/3056 2023 2023 University of Mosul, department of computer science and mathematics, Mosul, Iraq Khaled Khaled A k-arc in a plane PG (2, q) is a set of k point such that every line in the plane intersect it in at most two points and there is a line intersect it in exactly two points. A k-arc is complete if there is no k+1-arc containing it. This thesis is concerned with studies a k-arcs, k=4, 5,…., 10 and classification of protectively distinct k-arcs and distinct arcs under collineation. We prove by using computer program that the only complete k-arcs is for, k= 6, 10. 2024 2024 1 8 10.54216/NIF.030201 https://www.americaspg.com/articleinfo/39/show/3056