Paper Title
Powers of Cycle Graph Which are k-Self Complementary and k-Co-Self Complementary

Abstract
E Sampath Kumar and L Pushpalatha [2], defined a new type of complement as follows; Let G = (V,E) be a graph and P ={V_1,V_2,…,V_k} be a partition of V of order k ≥ 1. The k-complement G_k^P of G (with respect to P) is defined as follows: For all V_i and V_j in P,i ≠j, remove the edges between V_i and V_j , and add the edges which are not in G. The graph G is k-self complementary (k-s.c.) with respect to P if G_k^P≅G. A graph G is k-co-self complementary (k-co.s.c.) if G_k^P≅G ̅. The m^thpower G^m of an undirected graph G is another graph that has the same set of vertices, but in which two vertices are adjacent when their distance in G is at most k. In this paper, we obtain some results on the k-self complementary and k-co-self complementary powers cycle graph. Also we obtain all C_n^2 which are k-self complementary and k-co-self complementary. Keywords - k-complement, k-self complementary, k-co-self complementary, Powers of Cycle Graph.