On k-complementing permutations of cyclically k-complementary graphs Original Research Article

Let [Hini]ini,2,…,k be an isomorphic factorization of Kn where k ⩾ 2 and k divides 12n(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.