الملخص

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 projectively 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. This work take (150) hours computer time .