Abstract :
A tree containing exactly two nonpendant vertices is called a doublestar. Let $k_1$ and $k_2$ be two positive integers. The doublestar with degree sequence $(k_1+1, k_2+1, 1, ldots, 1)$ is denoted by $S_{k_1, k_2}$. It is known that a cubic graph has an $S_{1,1}$decomposition if and only if it contains a perfect matching. In this paper, we study the $S_{1,2}$decomposition of cubic graphs. We present some necessary and some sufficient conditions for the existence of an $S_{1, 2}$decomposition in cubic graphs.
