On the existence of 5-sun systems

A k -sun graph S ( C k ) is a graph obtained from a k -cycle by adding a pendent edge to each vertex of the k -cycle. A k -sun system of order v is a decomposition of the complete graph K v into k -sun graphs. In this paper, we find the necessary and sufficient condition for the existence of a 5-sun system of order v . Moreover, we obtain cyclic 5-sun systems when n ≡ 1 , 5 ( mod 20 ) and 1-rotational 5-sun systems when n ≡ 0 ( mod 20 ) .