On the existence of kk-sun systems

A kk-sun graph S(Ck)S(Ck) is obtained from the cycle of length kk, CkCk, by adding a pendant edge to each vertex of CkCk. A kk-sun system of order vv is a decomposition of the complete graph KvKv into kk-sun graphs. In this paper, we use a difference method to obtain kk-sun systems of all possible orders for k=6,10,14k=6,10,14 and 2t2t where tt is a positive integer at least 2. More precisely, we obtain cyclic kk-sun systems of odd order and 1-rotational kk-sun systems of even order when the order is greater than 4k4k.