Greedy cycles in the star graphs

We apply the greedy approach to construct greedy cycles in Star graphs $S_n, n\geqslant 3,$ defined as Cayley graphs on the symmetric group $\mathrm{Sym}_n$ with generating set $t=\{(1\,i),2\leqslant i\leqslant n\}$ of transpositions. We define greedy sequences presented by distinct elements from $t$, and prove that any greedy sequence of length $k$, $2\leqslant k\leqslant n-1$, forms a greedy cycle of length $2\cdot3^{k-1}$. Based on these greedy sequences we give a construction of a maximal set of independent greedy cycles in the Star graphs $S_n$ for any $n\geqslant 3$.