Near automorphisms of cycles

Let ff be a permutation of V(G)V(G). Define δf(x,y)=|dG(x,y)-dG(f(x),f(y))|δf(x,y)=|dG(x,y)-dG(f(x),f(y))| and δf(G)=∑δf(x,y)δf(G)=∑δf(x,y) over all the unordered pairs {x,y}{x,y} of distinct vertices of G  . Let π(G)π(G) denote the smallest positive value of δf(G)δf(G) among all the permutations f   of V(G)V(G). The permutation f   with δf(G)=π(G)δf(G)=π(G) is called a near automorphism of G  . In this paper, we study the near automorphisms of cycles CnCn and we prove that π(Cn)=4⌊n/2⌋-4π(Cn)=4⌊n/2⌋-4, moreover, we obtain the set of near automorphisms of CnCn.