On the existence of 5-sun systems

A kk-sun graph S(Ck)S(Ck) is a graph obtained from a kk-cycle by adding a pendent edge to each vertex of the kk-cycle. A kk-sun system of order vv is a decomposition of the complete graph KvKv into kk-sun graphs. In this paper, we find the necessary and sufficient condition for the existence of a 5-sun system of order vv. Moreover, we obtain cyclic 5-sun systems when n≡1,5(mod20) and 1-rotational 5-sun systems when n≡0(mod20).