On k-complementing permutations of cyclically k-complementary graphs

Let {Hi}i, 2, ..., k be an isomorphic factorization of Kn where k greater than or equal 2 and k divides 1/2n(n - 1). If there is a permutation β on V(Kn) such that β:V(Hti) -> V(Hti+1) is an isomorphism for i = 1, 2, ..., k - 1 where {Hti}i = 1, 2, ..., k is a rearrangement of {Hi}i = 1, 2, ...,k then a graph G of order n isomorphic to Hi is called a cyclically k-complementary graph. We call the aforementioned permutation β a k-complementing permutation of a cyclically k-complementary graph. The purpose of this paper is to present some properties of k-complementing permutations of the said graphs.