Near automorphisms of the complement or the square of a cycle.

Let G be a graph with vertex set V (G), f a permutation of V (G). Define δf(x,y) = |d(x,y) − d(f(x),f(y))| and δf(G) =∑ δf(x,y), where the sum is taken over all unordered pairs x, y of distinct vertices of G. Let π(G) denote the smallest positive value of δf(G) among all permutations f of V (G). A permutation f with δf(G) = π(G) is called a near automorphism of G. In this paper, the near automorphisms of the complement or the square of a cycle are characterized. Moreover, π(Cn¯) and π Cn2 are determined. [ABSTRACT FROM AUTHOR]