$(13)$ Use the sorted edges algorithm to find a Hamiltonian cycle in the graph below Be sure to show which edges you choose to include in the cycle.

$RS=1$

$OQ=2$

$SN=3$

$NR=4$

$RQ=5$

$OR=6$

$OS=7$

$OP=8$

$ON=9$

$NP=10$

$NQ=11$

$PQ=12$