Near automorphisms of cycles

Let f be a permutation of V(G). Define @d"f(x,y)=|d"G(x,y)-d"G(f(x),f(y))| and @d"f(G)[email protected][email protected]"f(x,y) over all the unordered pairs {x,y} of distinct vertices of G. Let @p(G) denote the smallest positive value of @d"f(G) among all the permutations f of V(G). The permutation f with @d"f(G)[email protected](G) is called a near automorphism of G. In this paper, we study the near automorphisms of cycles C"n and we prove that @p(C"n)[email protected]?n/[email protected]?-4, moreover, we obtain the set of near automorphisms of C"n.