On the existence of -sun systems

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